293 research outputs found
Vanishing viscosity limits for the degenerate lake equations with Navier boundary conditions
The paper is concerned with the vanishing viscosity limit of the
two-dimensional degenerate viscous lake equations when the Navier slip
conditions are prescribed on the impermeable boundary of a simply connected
bounded regular domain. When the initial vorticity is in the Lebesgue space
with , we show the degenerate viscous lake equations
possess a unique global solution and the solution converges to a corresponding
weak solution of the inviscid lake equations. In the special case when the
vorticity is in , an explicit convergence rate is obtained
Stability with respect to domain of the low Mach number limit of compressible viscous fluids
We study the asymptotic limit of solutions to the barotropic Navier-Stokes
system, when the Mach number is proportional to a small parameter \ep \to 0
and the fluid is confined to an exterior spatial domain \Omega_\ep that may
vary with \ep. As , it is shown that the fluid
density becomes constant while the velocity converges to a solenoidal vector
field satisfying the incompressible Navier-Stokes equations on a limit domain.
The velocities approach the limit strongly (a.a.) on any compact set, uniformly
with respect to a certain class of domains. The proof is based on spectral
analysis of the associated wave propagator (Neumann Laplacian) governing the
motion of acoustic waves.Comment: 32 page
Existence of weak solution for compressible fluid models of Korteweg type
This work is devoted to prove existence of global weak solutions for a
general isothermal model of capillary fluids derived by J.- E Dunn and J.
Serrin (1985) [6], which can be used as a phase transition model. We improve
the results of [5] by showing the existence of global weak solution in
dimension two for initial data in the energy space, close to a stable
equilibrium and with specific choices on the capillary coefficients. In
particular we are interested in capillary coefficients approximating a constant
capillarity coefficient. To finish we show the existence of global weak
solution in dimension one for a specific type of capillary coefficients with
large initial data in the energy space
Existence of global strong solutions in critical spaces for barotropic viscous fluids
This paper is dedicated to the study of viscous compressible barotropic
fluids in dimension . We address the question of the global existence
of strong solutions for initial data close from a constant state having
critical Besov regularity. In a first time, this article show the recent
results of \cite{CD} and \cite{CMZ} with a new proof. Our result relies on a
new a priori estimate for the velocity, where we introduce a new structure to
\textit{kill} the coupling between the density and the velocity as in
\cite{H2}. We study so a new variable that we call effective velocity. In a
second time we improve the results of \cite{CD} and \cite{CMZ} by adding some
regularity on the initial data in particular is in . In this
case we obtain global strong solutions for a class of large initial data on the
density and the velocity which in particular improve the results of D. Hoff in
\cite{5H4}. We conclude by generalizing these results for general viscosity
coefficients
Recent Advances Concerning Certain Class of Geophysical Flows
This paper is devoted to reviewing several recent developments concerning
certain class of geophysical models, including the primitive equations (PEs) of
atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for
large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes
equations coupled to the heat convection by adopting the Boussinesq and
hydrostatic approximations, while the tropical atmosphere model considered here
is a nonlinear interaction system between the barotropic mode and the first
baroclinic mode of the tropical atmosphere with moisture.
We are mainly concerned with the global well-posedness of strong solutions to
these systems, with full or partial viscosity, as well as certain singular
perturbation small parameter limits related to these systems, including the
small aspect ratio limit from the Navier-Stokes equations to the PEs, and a
small relaxation-parameter in the tropical atmosphere model. These limits
provide a rigorous justification to the hydrostatic balance in the PEs, and to
the relaxation limit of the tropical atmosphere model, respectively. Some
conditional uniqueness of weak solutions, and the global well-posedness of weak
solutions with certain class of discontinuous initial data, to the PEs are also
presented.Comment: arXiv admin note: text overlap with arXiv:1507.0523
Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon
This paper deals with the dead-water phenomenon, which occurs when a ship
sails in a stratified fluid, and experiences an important drag due to waves
below the surface. More generally, we study the generation of internal waves by
a disturbance moving at constant speed on top of two layers of fluids of
different densities. Starting from the full Euler equations, we present several
nonlinear asymptotic models, in the long wave regime. These models are
rigorously justified by consistency or convergence results. A careful
theoretical and numerical analysis is then provided, in order to predict the
behavior of the flow and in which situations the dead-water effect appears.Comment: To appear in Nonlinearit
The sharp-interface limit for the Navier--Stokes--Korteweg equations
We investigate the sharp-interface limit for the Navier--Stokes--Korteweg model, which is an extension of the compressible Navier--Stokes equations. By means of compactness arguments, we show that solutions of the Navier--Stokes--Korteweg equations converge to solutions of a physically meaningful free-boundary problem. Assuming that an associated energy functional converges in a suitable sense, we obtain the sharp-interface limit at the level of weak solutions
Recommended from our members
Final Version Zurich, 27th July 2010
Adaptation to climate change requires an integrated risk management approach, including risk
assessment, prevention and insurance. Insurance solutions can potentially provide a significant
contribution in expanding and strengthening adaptation response to climate change risks.
Numerous proposals and submissions under the United Nations Framework Convention on
Climate Change (UNFCCC) make reference to risk transfer and insurance solutions as a com-
plementary element of a systematic adaptation approach, but no consensus has been achieved
regarding their role and eventual implementation under UNFCCC.
This paper intends to raise awareness on existing work and the current challenges related to
climate relevant insurance, in developing countries and to contribute to a further discussion of
the insurance topic under UNFCCC.
Past experiences and discussions can provide a framework for larger policies on the role of
insurance in the emerging climate financing architecture. Further pilot implementation, research,
and systematic learning is required. Many of the elements such as data collection, research, ca-
pacity building and exploration of public private partnerships are valuable for achieving broader
adaptation objectives. It is therefore encouraged that the Parties further explore and define the
scope of insurance solutions as part of climate change adaptation
Impact Forecasting to Support Emergency Management of Natural Hazards
Forecasting and early warning systems are important investments to protect lives, properties, and livelihood. While early warning systems are frequently used to predict the magnitude, location, and timing of potentially damaging events, these systems rarely provide impact estimates, such as the expected amount and distribution of physical damage, human consequences, disruption of services, or financial loss. Complementing early warning systems with impact forecasts has a twofold advantage: It would provide decision makers with richer information to take informed decisions about emergency measures and focus the attention of different disciplines on a common target. This would allow capitalizing on synergies between different disciplines and boosting the development of multihazard early warning systems. This review discusses the state of the art in impact forecasting for a wide range of natural hazards. We outline the added value of impact-based warnings compared to hazard forecasting for the emergency phase, indicate challenges and pitfalls, and synthesize the review results across hazard types most relevant for Europe
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