Existence of Solutions for Three Dimensional Stationary Incompressible Euler Equations with Nonvanishing Vorticity

In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.

Convergence of the Vlasov-Poisson-Boltzmann System to the Incompressible Euler Equations

In this paper we establish the convergence of the Vlasov-Poisson-Boltzmann system to the incompressible Euler equations in the so-called quasi-neutral regime. The convergence is rigorously proved for time intervals on which the smooth solution of the Euler equations of the incompressible fluid exists. The proof relies on the relative-entropy method.

On the Free Boundary to the Incompressible Euler Equations

In this paper, we consider an inviscid, incompressible, irrotational fluid in a region of R^3 with free boundary. Motivated by [1], we find that in this particular case, we do not need the complicated energy functional in [1], instead we can use a simpler replacement and get the a priori energy estimate for a positive time, which depends only on the initial data.

ON A NEW 3D MODEL FOR INCOMPRESSIBLE EULER AND NAVIER-STOKES EQUATIONS

In this paper, we investigate some new properties of the incompressible Euler and Navier-Stokes equations by studying a 3D model for axisymmetric 3D incompressible Euler and Navier-Stokes equations with swirl. The 3D model is derived by reformulating the axisymmetric 3D incompressible Euler and Navier-Stokes equations and then neglecting the convection term of the resulting equations. Some properties of this 3D model are reviewed. Finally, some potential features of the incompressible Euler and Navier-Stokes equations such as the stabilizing effect of the convection are presented.

GEVREY REGULARITY WITH WEIGHT FOR INCOMPRESSIBLE EULER EQUATION IN THE HALF PLANE

In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L;-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.

THE EULER EQUATION AND ONSAGER CONJECTURE

In this paper, we introduce the progress of the Euler equation and Onsager conjecture. We also introduce the Euler＇s life, the researches about the incompressible Euler equation, and the Onsager conjecture.

On the local wellposedness of 3-D water wave problem with vorticity

In this article, we first present an equivalent formulation of the free boundary problem to 3-D incompressible Euler equations, then we announce our local wellposedness result concerning the free boundary problem in Sobolev space provided that there is no self-intersection point on the initial surface and under the stability assumption that $\frac{{\partial p}}{{\partial n}}(\xi )\left| {_{t = 0} } \right. \leqslant - 2c_0 < 0$ being restricted to the initial surface.

Asymptotic limit of the Gross-Pitaevskii equation with general initial data

This paper mainly concerns the mathematical justification of the asymptotic limit of the GrossPitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.

Paralinearization of the Dirichlet-Neumann operator and applications to progressive gravity waves Dedicated to the NSFC-CNRS Chinese-French summer institute on fluid mechanics in 2010

This note presents a paradifferential approach to the analysis of the water waves equations.