Stability of the Poho\v{z}aev obstrucion in dimension 3

We investigate problems connected to the stability of the wellknown Poho\v{z}aev obstruction. We generalize results which were obtained in the minimizing setting by Brezis and Nirenberg [2] and more recently in the radial situation by Brezis and Willem [3].Comment: arXiv admin note: text overlap with arXiv:2211.0059

Les phases d’incision de la vallée de la Marne entre Joinville et Vitry-le-François(Est du bassin parisien / France)

L’article porte sur l’analyse de l’incision de la vallée de la Marne, notamment sur la recherche et l’analyse des stades d’incision entre Joinville et Vitry-le-François, dans la traversée du plateau calcaire du Barrois et la dépression alluviale du Perthois. Le levé de la carte géomorphologique a permis de mettre en évidence sept niveaux d’incision visibles aujourd’hui dans le paysage par des formes de versants et/ou de terrasses. Ces sept niveaux peuvent être regroupés en trois familles de formes dont la construction s’étale sur la période « plio-quaternaire ». L’incision totale est de l’ordre de 200 m. Par ailleurs, un passage de la Marne vers le nord, en direction de la vallée de l’Aisne via les paléo-vallées de la Saulx et de l’Ornain, avait été envisagé par le fossé tectonique de Cousance et par la Forêt de Trois-Fontaines dès la fin du XIXe siècle. Les levés effectués montrent que dès la fin de la période de construction de la première famille de formes, la Marne avait un tracé suivant sa vallée actuelle en amont deSaint-Dizier. Le fossé de Cousancea donc été creusé par le jeu de l’érosion différentielle. L’hypothèse d’un paléo-tracé de la Marne par ce passage paraît donc devoir être abandonnée.The paper focuses on the analysis of the incision of the valley of the Marne, in particular on research and analysis of incision stages between Joinville and Vitry-le-François, where it traverses the Barrois limestone plateau and the alluvial plain of Perthois. Geomorphological mapping of slopes and/or terrace forms has revealed seven incision levels visible today in the landscape. These seven levels can be subdivised into three groups, the construction of which extends across the “Plio-Quaternary” period, with a total amount of incision in the order of 200 m. By the end of the nineteenth century, a northward passage of the Marne, in the direction of the Aisne valley via the palaeovalleys of the Saulx and the Ornain, had been envisaged through the Cousance trough and the « Forêt de Trois Fontaines ». The surveys carried out for this study show that, from the end of the period of construction of the first group of forms, the Marne followed a route along its present valley upstream of Saint-Dizier. The Cousance trough has therefore been cut by the action of differential erosion. The hypothesis of a palaeo-route of the Marne via this passage must therefore be abandoned.Der Artikel handelt von der Analyse der Eintiefung des Marnetals, insbesondere von der Untersuchung und Analyse der Eintiefungsstadien zwischen Joinville und Vitry-le-François im Übergang vom Kalkplateau des Barrois zur Alluvial-depression des Perthois. Die Aufnahme der geomorphologischen Karte hat sieben Eintiefungsniveaus deutlich gemacht, die heute in der Landschaft durch Hang- und Terrassenformen sichtbar sind. Diese sieben Niveaus können in drei Formfamilien gruppiert werden, deren Bildung sich über die Plio-Quartär-Periode erstreckt. Die gesamte Eintiefung beträgt etwa 200 m in der Region. Zudem wurde seit Ende des 19. Jahrhunderts ein Übergang der Marne nach Norden in Richtung des Aisnetals über die Paläotäler der Saulx und des Ornain in Betracht gezogen – durch den tektonischen Graben von Cousance und die Forêt des Trois Fontaines. Die Erhebungen zeigen, dass seit dem Ende der Ausbildungsperiode der ersten Formengeneration die Marne einen Verlauf hatte, der dem aktuellen des Tales flussaufwärts von Saint-Dizier folgt. Der Graben von Cousance wurde also durch das differenzierte Spiel der Erosion eingeschnitten. Die Hypothese von einem alten Verlauf der Marne durch diese Passage muss somit wohl verlassen werden

Les phases d’incision de la vallée de la Marne entre Joinville et Vitry-le-François(Est du bassin parisien / France)

L’article porte sur l’analyse de l’incision de la vallée de la Marne, notamment sur la recherche et l’analyse des stades d’incision entre Joinville et Vitry-le-François, dans la traversée du plateau calcaire du Barrois et la dépression alluviale du Perthois. Le levé de la carte géomorphologique a permis de mettre en évidence sept niveaux d’incision visibles aujourd’hui dans le paysage par des formes de versants et/ou de terrasses. Ces sept niveaux peuvent être regroupés en trois familles de formes dont la construction s’étale sur la période « plio-quaternaire ». L’incision totale est de l’ordre de 200 m. Par ailleurs, un passage de la Marne vers le nord, en direction de la vallée de l’Aisne via les paléo-vallées de la Saulx et de l’Ornain, avait été envisagé par le fossé tectonique de Cousance et par la Forêt de Trois-Fontaines dès la fin du XIXe siècle. Les levés effectués montrent que dès la fin de la période de construction de la première famille de formes, la Marne avait un tracé suivant sa vallée actuelle en amont deSaint-Dizier. Le fossé de Cousancea donc été creusé par le jeu de l’érosion différentielle. L’hypothèse d’un paléo-tracé de la Marne par ce passage paraît donc devoir être abandonnée.The paper focuses on the analysis of the incision of the valley of the Marne, in particular on research and analysis of incision stages between Joinville and Vitry-le-François, where it traverses the Barrois limestone plateau and the alluvial plain of Perthois. Geomorphological mapping of slopes and/or terrace forms has revealed seven incision levels visible today in the landscape. These seven levels can be subdivised into three groups, the construction of which extends across the “Plio-Quaternary” period, with a total amount of incision in the order of 200 m. By the end of the nineteenth century, a northward passage of the Marne, in the direction of the Aisne valley via the palaeovalleys of the Saulx and the Ornain, had been envisaged through the Cousance trough and the « Forêt de Trois Fontaines ». The surveys carried out for this study show that, from the end of the period of construction of the first group of forms, the Marne followed a route along its present valley upstream of Saint-Dizier. The Cousance trough has therefore been cut by the action of differential erosion. The hypothesis of a palaeo-route of the Marne via this passage must therefore be abandoned.Der Artikel handelt von der Analyse der Eintiefung des Marnetals, insbesondere von der Untersuchung und Analyse der Eintiefungsstadien zwischen Joinville und Vitry-le-François im Übergang vom Kalkplateau des Barrois zur Alluvial-depression des Perthois. Die Aufnahme der geomorphologischen Karte hat sieben Eintiefungsniveaus deutlich gemacht, die heute in der Landschaft durch Hang- und Terrassenformen sichtbar sind. Diese sieben Niveaus können in drei Formfamilien gruppiert werden, deren Bildung sich über die Plio-Quartär-Periode erstreckt. Die gesamte Eintiefung beträgt etwa 200 m in der Region. Zudem wurde seit Ende des 19. Jahrhunderts ein Übergang der Marne nach Norden in Richtung des Aisnetals über die Paläotäler der Saulx und des Ornain in Betracht gezogen – durch den tektonischen Graben von Cousance und die Forêt des Trois Fontaines. Die Erhebungen zeigen, dass seit dem Ende der Ausbildungsperiode der ersten Formengeneration die Marne einen Verlauf hatte, der dem aktuellen des Tales flussaufwärts von Saint-Dizier folgt. Der Graben von Cousance wurde also durch das differenzierte Spiel der Erosion eingeschnitten. Die Hypothese von einem alten Verlauf der Marne durch diese Passage muss somit wohl verlassen werden

Altimetry for the future: Building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the ‘‘Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Altimetry for the future: building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the “Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Comportement asymptotique des surfaces à courbure moyenne constante

Dans cette thèse on étudie le comportement asymptotique des suites de surfaces à courbure moyenne constante. Plus précisément, on développe une analyse de blow-up pour l'équation générale des surfaces à courbure moyenne constante qui nous permet de localiser le lieux de concentration des suites de surface à grande courbure moyenne constante dans une variété courbée ou un domaine de l'espace euclidien. D'autre part, on démontre également dans ce manuscrit un certain nombre d'obstructions concernant la courbure moyenne d'une surface générale.In this thesis we study the asymptotic behavior of sequences of constant mean curvature surfaces. Specifically, we develop an analysis of blow-up for the general equation of constant mean curvature surfaces, which allows us to locate the places of concentration of sequences of surface with large constant mean curvature in a curved manifold or in a domain of the Euclidean space. On the other hand, it is also shows in this manuscript some obstructions on the mean curvature of a general surface.LYON-ENS Sciences (693872304) / SudocSudocFranceF

IWV retrieval from ground and shipborne GPS receivers during NAWDEX

International audience<p>For the documentation of time and space variations of water vapor in atmosphere during the Nawdex campaign (North Atlantic, Autumn 2016), a ground network of more than 1200 coastal continuously operation reference GNSS stations has been analyzed. This network spreads from Caribbeans to Morocco through Greenland. Retrieved IWV have been used to evaluate ERAI and ERA5 reanalysis and highlight improvements made by ERA5 (-0.2 +/- 1.6 kg/m2 vs -0.3 +/- 2.1 kg/m2 overall). They are also used to describe high impact weather events that took place during the experiment.</p><p>The analysis of this ground GNSS network has been completed with the IWV retrieved from GPS data acquired by the French RV Atalante which cruises in the area during the experiment. IWV from shipborne receiver are consistent with both ERAI and ERA5 reanalysis (1.0 +/- 3.2 kg/m2 and 1.3 +/- 2.0 kg/m2 respectively) ; shipborne IWV also agree with IWV from nearby ground GNSS stations (-0.4 +/- 0.9 kg/m2). These results confirm the quality of shipborne IWV retrievals and opens up prospects for use in climatology and meteorology.</p&gt

IWV retrieval from shipborne GPS receiver on hydrographic ship Borda

International audience<p>This work aims to provide a quick review of different experiments conducted in the past for the estimation of integrated water vapor content from shipborne GNSS receiver. This state of the art will be confronted with results obtained using GPS data acquired by the French Hydrographic Ship Borda on a cruise over Atlantic Ocean and Mediterranean Sea, from Brest to Toulon in August 2015; the estimated IWV are compared with satellite observations (MODIS) and outputs from numerical weather prediction models (ERAI, ERA5, Arpege, Arome); while differences between GPS and MODIS retrievals reach almost 4 kg/m2 in terms of RMS, agreement is generally much better with numerical models (2 up to 3 kg/m2 in terms of RMS). Use of real-time orbit and clocks product is also investigated in order to assess the performance of near real-time GPS-IWV estimation for NWP purposes. We will draw out the prospects in terms of possibilities and opportunities for the use of shipborne GNSS IWV for meteorology and climatology.</p&gt