On the Cauchy problem for the magnetic Zakharov system

In this paper, we study the Cauchy problem of the magnetic type Zakharov system which describes the pondermotive force and magnetic field generation effects resulting from the non-linear interaction between plasma-wave and particles. By using the energy method to derive a priori bounds and an approximation argument for the construction of solutions, we obtain local existence and uniqueness results for the magnetic Zakharov system in the case of $d=2,3$

Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption

We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy at most slightly above that of the ground state.Comment: 40 page

On the 2d Zakharov system with L^2 Schr\"odinger data

We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L^2 x H^{-1/2} x H^{-3/2}. This is the space of optimal regularity in the sense that the data-to-solution map fails to be smooth at the origin for any rougher pair of spaces in the L^2-based Sobolev scale. Moreover, it is a natural space for the Cauchy problem in view of the subsonic limit equation, namely the focusing cubic nonlinear Schroedinger equation. The existence time we obtain depends only upon the corresponding norms of the initial data - a result which is false for the cubic nonlinear Schroedinger equation in dimension two - and it is optimal because Glangetas-Merle's solutions blow up at that time.Comment: 30 pages, 2 figures. Minor revision. Title has been change

Strichartz estimates on Schwarzschild black hole backgrounds

We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of earlier work of Metcalfe-Tataru, in order to establish global-in-time Strichartz estimates. A considerable part of the paper is devoted to a precise analysis of solutions near the trapping region, namely the photon sphere.Comment: 44 pages; typos fixed, minor modifications in several place

Fundamental Solutions for the Klein-Gordon Equation in de Sitter Spacetime

In this article we construct the fundamental solutions for the Klein-Gordon equation in de Sitter spacetime. We use these fundamental solutions to represent solutions of the Cauchy problem and to prove $L^p-L^q$ estimates for the solutions of the equation with and without a source term

Crustal structure of the Peruvian continental margin from wide-angle seismic studies

Active seismic investigations along the Pacific margin off Peru were carried out using ocean bottom hydrophones and seismometers. The structure and the P-wave velocities of the obliquely subducting oceanic Nazca Plate and overriding South American Plate from 8°S to 15°S were determined by modelling the wide-angle seismic data combined with the analysis of reflection seismic data. Three detailed cross-sections of the subduction zone of the Peruvian margin and one strike-line across the Lima Basin are presented here. The oceanic crust of the Nazca Plate, with a thin pelagic sediment cover, ranging from 0–200 m, has an average thickness of 6.4 km. At 8°S it thins to 4 km in the area of Trujillo Trough, a graben-like structure. Across the margin, the plate boundary can be traced to 25 km depth. As inferred from the velocity models, a frontal prism exists adjacent to the trench axis and is associated with the steep lower slope. Terrigeneous sediments are proposed to be transported downslope due to gravitational forces and comprise the frontal prism, characterized by low seismic P-wave velocities. The lower slope material accretes against a backstop structure, which is defined by higher seismic P-wave velocities, 3.5–6.0 km s−1. The large variations in surface slope along one transect may reflect basal removal of upper plate material, thus steepening the slope surface. Subduction processes along the Peruvian margin are dominated by tectonic erosion indicated by the large margin taper, the shape and bending of the subducting slab, laterally varying slope angles and the material properties of the overriding continental plate. The erosional mechanisms, frontal and basal erosion, result in the steepening of the slope and consequent slope failure

Global well-posedness for a coupled modified kdv system

We prove the sharp global well-posedness result for the initial value problem (IVP) associated to the system of the modi ed Korteweg-de Vries (mKdV) equation. For the single mKdV equation such result has been obtained by using Mirura's Transform that takes the KdV equation to the mKdV equation [8]. We do not know the existence of Miura's Transform that takes a KdV system to the system we are considering. To overcome this di culty we developed a new proof of the sharp global well-posedness result for the single mKdV equation without using Miura's Transform. We could successfully apply this technique in the case of the mKdV system to obtain the desired result.Fundação para a Ciência e a Tecnologia (FCT