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# Search results

12,381 records were found.

## Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation

Comment: 32 pages. Published version with a few typos fixed

## Aubry-Mather measures in the non convex setting

Comment: final version

## Vorticity internal transition layers for the Navier-Stokes equations

We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show -thanks to an asymptotic expansion- that there is a sharp but smooth variation of the fluid vorticity into a internal layer moving with the flow of the Euler equations; as long as this later exists and as t * nu is small, where nu is the viscosity coefficient.

## Geometric property of the Ground State Eigenfunction for Cauchy Process

Comment: 25 pages

## Nonlocal Crowd Dynamics Models for several Populations

This paper develops the basic analytical theory related to some recently introduced crowd dynamics models. Where well posedness was known only locally in time, it is here extended to all of $\reali^+$. The results on the stability with respect to the equations are improved. Moreover, here the case of several populations is considered, obtaining the well posedness of systems of multi-D non-local conservation laws. The basic analytical tools are provided by the classical Kruzkov theory of scalar conservation laws in several space dimensions.

## Global well posedness for the Navier-Stokes equations

Comment: 10 pages

## A decomposition approach for the discrete-time approximation of FBSDEs with a jump I : the Lipschitz case

We study the discrete-time approximation for solutions of forward-backward stochas- tic dierential equations (FBSDEs) with a jump. In this part, we study the case of Lipschitz generators, and we refer to the second part of this work [15] for the quadratic case. Our method is based on a result given in the companion paper [14] which allows to link a FBSDE with a jump with a recursive system of Brownian FBSDEs. Then we use the classical results on discretization of Brownian FBSDEs to approximate the recursive system of FBSDEs and we recombine these approximations to get a dis- cretization of the FBSDE with a jump. This approach allows to get a convergence rate similar to that of schemes for Brownian FBSDEs.

## Center Manifold: a case study

Comment: 24 pages

## Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves

This paper is concerned with a priori $C^\infty$ regularity for three-dimensional doubly periodic travelling gravity waves whose fundamental domain is a symmetric diamond. The existence of such waves was a long standing open problem solved recently by Iooss and Plotnikov. The main difficulty is that, unlike conventional free boundary problems, the reduced boundary system is not elliptic for three-dimensional pure gravity waves, which leads to small divisors problems. Our main result asserts that sufficiently smooth diamond waves which satisfy a diophantine condition are automatically $C^\infty$. In particular, we prove that the solutions defined by Iooss and Plotnikov are $C^\infty$. Two notable technical aspects are that (i) no smallness condition is required and (ii) we obtain an exact paralinearization formula for the Dirichlet to...

## Penalization approach for mixed hyperbolic systems with constant coefficients satisfying a Uniform Lopatinski Condition

In this paper, we describe a new, systematic and explicit way of approximating solutions of mixed hyperbolic systems with constant coefficients satisfying a Uniform Lopatinski Condition via different Penalization approaches.