相关论文: On admissibility criteria for weak solutions of th…
We deal with entropy solutions to the Cauchy problem for the isentropic compressible Euler equations in the space-periodic case. In more than one space dimension, the methods developed by De Lellis-Sz\'ekelyhidi enable us to show failure of…
In this article, we will study unbounded solutions of the 2D incompressible Euler equations. One of the motivating factors for this is that the usual functional framework for the Euler equations (e.g. based on finite energy conditions, such…
The Euler system in fluid dynamics is a model of a compressible inviscid fluid incorporating the three basic physical principles: Conservation of mass, momentum, and energy. We show that the Cauchy problem is basically ill-posed for the…
We give a new sufficient criteria to prove the uniqueness of the incompressible Euler equation in dimension $N\geq2$. In their celebrated works by V. Scheffer [18], A. Shnirelman [19], C. De Lellis and L. Sz\'ekelyhidi Jr. [7] they have…
In Part I of the paper, we prove non-uniqueness of the solution to the Cauchy problem of the Euler equations of an ideal incompressible fluid in dimension two with vorticity in some Lebesgue space. The radially symmetric external force is…
In this paper, we study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We prove the existence and uniqueness of global solutions in critical Besov spaces to the considered system with small…
We establish a complete picture for existence, uniqueness, and representation of weak solutions to non-autonomous parabolic Cauchy problems of divergence type. The coefficients are only assumed to be uniformly elliptic, bounded, measurable,…
We start with the classic result that the Cauchy problem for ideal compressible gas dynamics is locally well posed in time in the sense of Hadamard; there is a unique solution that depends continuously on initial data in Sobolev space $H^s$…
We consider several pressureless variants of the compressible Euler equation driven by nonlocal repulsionattraction and alignment forces with Poisson interaction. Under an energy admissibility criterion, we prove existence of global…
We consider the Cauchy problem for the isentropic compressible Euler-Maxwell equations under general pressure laws in a three-dimensional periodic domain. For any smooth initial electron density away from the vacuum and smooth…
We study the Cauchy problem for the isentropic hypo-viscous compressible Navier-Stokes equations (CNS) under general pressure laws in all dimensions $d\geq 2$. For all hypo-viscosities $(-\Delta)^\alpha$ with $\alpha\in (0,1)$, we prove…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
We consider the Cauchy problem for wave equations with unbounded damping coefficients in the whole space. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence…
We consider the total energy decay together with L^2-bound of the solution itself of the Cauchy problem for wave equations with a localized damping and a short-range potential. We treat it in the one dimensional Euclidean space R. We adopt…
We consider the 2-d isentropic compressible Euler equations. It was shown in by E. Chiodaroli, C. De Lellis and O. Kreml that there exist Riemann initial data as well as Lipschitz initial data for which there exist infinitely many weak…
Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically…
In this paper we propose a new point of view on weak solutions of the Euler equations, describing the motion of an ideal incompressible fluid in $\mathbb{R}^n$ with $n\geq 2$. We give a reformulation of the Euler equations as a differential…
An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristics…
We are concerned with global finite-energy solutions of the three-dimensional compressible Euler-Poisson equations with gravitational potential and general pressure law, especially including the constitutive equation of white dwarf stars.…
We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial…