Related papers: The analytic structure of 2D Euler flow at short t…
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…
In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…
In this paper, we consider 2D incompressible Euler equations in an unbounded domain with a free surface and a fixed bottom at finite depth. The fluid motion is under the influence of gravity and surface tension. We construct initial data…
We prove long-term regularity of solutions of the one-fluid Euler-Maxwell system in 3 spatial dimensions, in the case of small initial data with nontrivial vorticity.
The existence and uniqueness of two dimensional steady compressible Euler flows past a wall or a symmetric body are established. More precisely, given positive convex horizontal veloicty in the upstream, there exists a critical value…
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…
We consider steady states of the incompressible Euler equation on two-dimensional domains. For non-radial analytic steady states on bounded simply connected domains, it was shown previously that there must be a global functional…
We give an elementary proof of long time inviscid damping for Sobolev perturbations near the Couette flow $(y,0)$ for the 2D Euler equations on $\mathbb{T} \times \mathbb{R}$. For any $s>1$ and any initial vorticity perturbation of size…
We study the subsonic flows governed by full Euler equations in the half plane bounded below by a piecewise smooth curve asymptotically approaching x1-axis. Nonconstant conditions in the far field are prescribed to ensure the real Euler…
We are interested in the stability analysis of two-dimensional incompressible inviscid fluids. Specifically, we revisit a recent result on the stability of Yudovich's solutions to the incompressible Euler equations in $L^\infty([0,T];H^1)$…
Incompressible 3D Euler equations develop high vorticity in very thin pancake-like regions from generic large-scale initial conditions. In this work we propose an exact solution of the Euler equations for the asymptotic pancake evolution.…
Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among…
The purpose of this paper is to study the phenomenon of singularity formation in large data problems for classical solutions to the Cauchy problem of the relativistic Euler equations. The classical theory established by P. D. Lax in 1964…
In [Lacave, IHP, ana, to appear (2008)] the author considered the two dimensional Euler equations in the exterior of a thin obstacle shrinking to a curve and determined the limit velocity. In the present work, we consider the same problem…
In this paper, we prove the linear damping for the 2-D Euler equations around a class of shear flows under the assumption that the linearized operator has no embedding eigenvalues. For the symmetric flows, we obtain the explicit decay…
A classical problem in fluid mechanics is the motion of an axisymmetric vortex sheet evolving under the action of surface tension, surrounded by an inviscid fluid. Lagrangian descriptions of these dynamics are well-known, involving complex…
We study the 2D incompressible Boussinesq equation without thermal diffusion, and aim to construct rigorous examples of small scale formations as time goes to infinity. In the viscous case, we construct examples of global smooth solutions…
The problem we are concerned with is whether singularities form in finite time in incompressible fluid flows. It is well known that the answer is ``no'' in the case of Euler and Navier-Stokes equations in dimension two. In dimension three…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations in an infinite cylinder are considered. It is shown that if the inflow-outflow is highly oscillating in time, the corresponding Euler flow cannot keep the…
We consider the 2D incompressible Navier-Stokes equations on $\mathbb{T}\times \mathbf{R}$, with initial vorticity that is $\delta$ close in $H^{log}_xL^2_{y}$ to $-1$(the vorticity of the Couette flow $(y,0)$). We prove that if $\delta\ll…