Related papers: The 2D Euler-Poisson System with Spherical Symmetr…
This paper is concerned with a two dimensional Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. We prove that the associated Cauchy problem is well-posed for initial data of low regularity, with…
We study the stabilizing effect of rotational forcing in the nonlinear setting of two-dimensional shallow-water and more general models of compressible Euler equations. In [H. Liu and E. Tadmor, Phys. D 188 (2004), no. 3-4, 262-276] we have…
Using a very high precision spectral calculation applied to the incompressible and inviscid flow with initial condition $\psi_0(x_1, x_2) = \cos x_1+\cos 2x_2$, we find that the width $\delta(t)$ of its analyticity strip follows a…
In this paper we study the equations governing the unsteady motion of an incompressible homogeneous generalized second grade fluid subject to periodic boundary conditions. We establish the existence of global-in-time strong solutions for…
This paper is concerned with the 2-dim two-phase interface Euler equation linearized at a pair of monotone shear flows in both fluids. We extend the Howard's Semicircle Theorem and study the eigenvalue distribution of the linearized Euler…
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…
Solutions of the Navier-Stokes and Euler equations with initial conditions for 2D and 3D cases were obtained in the form of converging series, by an analytical iterative method using Fourier and Laplace transforms \cite{TT10,TT11}. There…
Here we investigate global strong solutions for a class of partially dissipative hyperbolic systems in the framework of critical homogeneous Besov spaces. Our primary goal is to extend the analysis of our previous paper [10] to a functional…
In this {\bf draft version} we prove inhomogeneous Strichartz estimates with spherical symmetry in the abstract setting via duality arguments. Then we derive some new explicit estimates in the context of the wave equation. This allows us to…
This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths…
In this paper we study the existence of weak solutions to an unsteady system describing the motion of micro-polar electrorheological fluids. The constitutive relations for the stress tensors belong to the class of generalized Newtonian…
The purpose of this work is to prove existence of a weak solution of the two dimensional incompressible Euler equations on a noncylindrical domain consisting of a smooth, bounded, connected and simply connected domain undergoing a…
We prove global existence of weak solutions to two systems of equations which extend the dynamics of the Navier-Stokes equations for incompressible viscous flow with no-slip boundary condition. The systems of equations we consider arise as…
The Degasperis-Procesi equation is an approximating model of shallow-water wave propagating mainly in one direction to the Euler equations. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional…
We prove a definitive theorem on the asymptotic stability of point vortex solutions to the full Euler equation in 2 dimensions. More precisely, we show that a small, Gevrey smooth, and compactly supported perturbation of a point vortex…
We prove nonlinear asymptotic stability of a large class of monotonic shear flows among solutions of the 2D Euler equations in the channel $\mathbb{T}\times[0,1]$. More precisely, we consider shear flows $(b(y),0)$ given by a function $b$…
We study the existence and zero viscous limit of smooth solutions to steady compressible Navier-Stokes equations near plane shear flow between two moving parallel walls. Under the assumption $0<L\ll1$, we prove that for any plane supersonic…
The Euler-Maxwell system describes the evolution of a plasma when the collisions are important enough that each species is in a hydrodynamic equilibrium. In this paper we prove global existence of small solutions to this system set in the…
The main purpose of this paper is to formulate new conditions for smooth linearization of nonautonomous systems with discrete and continuous time. Our results assume that the linear part admits a nonuniform polynomial dichotomy and that the…
The existence of singular solutions of the incompressible Navier-Stokes system with singular external forces, the existence of regular solutions for more regular forces as well as the asymptotic stability of small solutions (including…