Existence of stationary vortex sheets for the 2D incompressible Euler equation

Stationary solutions for the 2D stochastic dis- sipative Euler equation

A 2-dimensional dissipative Euler equation, subject to a random perturbation is considered. Using compactness arguments, existence of martingale stationary solutions are proved. Mathematics Subject Classification (2000). Primary 60H15, Secondary 76D05.

Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets

We consider the free boundary problem for current-vortex sheets in ideal incompressible magnetohydrodynamics. The problem of current-vortex sheets arises naturally, for instance, in geophysics and astrophysics. We prove the existence of a unique solution to the constant-coefficient linearized problem and an a priori estimate with no loss of derivatives. This is a preliminary result to the study...

Integrable Structures for 2D Euler Equations of Incompressible Inviscid Fluids

The governing equation of turbulence, that we are interested in, is the incompressible 2D Navier– Stokes equation under periodic boundary conditions. We are particularly interested in investigating the dynamics of 2D Navier–Stokes equation in the infinite Reynolds number limit and of 2D Euler equation. Our approach is different from many other studies on 2D Navier–Stokes equation in which one s...

Quasilinear theory of the 2D euler equation

We develop a quasilinear theory of the 2D Euler equation and derive an integrodifferential equation for the evolution of the coarse-grained vorticity omega;(r,t). This equation respects all of the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel. We show under which hypothesis we can derive an H theorem for the Fermi...

Weak Solutions to the Stationary Incompressible Euler Equations