Related papers: Weak-Strong Uniqueness for the Isentropic Euler Eq…

In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position…

We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test…

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…

We prove the existence of a weak solution to the equations describing the inertial motions of a coupled system constituted by a rigid body containing a viscous compressible fluid. We then provide a weak-strong uniqueness result that allows…

We consider admissible weak solutions to the compressible Euler system with source terms, which include rotating shallow water system and the Euler system with damping as special examples. In the case of anti-symmetric sources such as…

This paper is concerned with the existence of compactly supported admissible solutions to the Cauchy problem for the isentropic compressible Euler equations. In more than one space dimension, convex integration techniques developed by De…

We prove the weak-strong uniqueness for measure-valued solutions of the incompressible Euler equations. These were introduced by R.DiPerna and A.Majda, and in particular global existence to any L2 initial data was proven. Whether…

In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$, by constructing some new control functions ingeniously, we obtain the lower bounds estimates…

This paper is concerned with the Riemann problem for the two-dimensional barotropic compressible Euler system with a general strictly increasing pressure law. By means of convex integration, the existence of infinitely many admissible weak…

We consider the Cauchy problem for the isentropic compressible Euler equations in a three-dimensional periodic domain under general pressure laws. For any smooth initial density away from the vacuum, we construct infinitely many entropy…

We show that any dissipative (measure-valued) solution of the compressible Euler system that complies with Dafermos' criterion of maximal dissipation is necessarily an admissible weak solution. In addition, we propose a simple, at most two…

This paper concerns with the compressible two-fluid model with algebraic pressure closure. We prove a conditional weak-strong uniqueness principle, meaning that a finite energy weak solution, with bounded densities, coincides with the…

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…

In this paper, we showed that for some given suitable density and pressure, there exist infinitely many compactly supported solutions with prescribed energy profile. The proof is mainly based on the convex integration scheme. We construct…

In this article, the weak-strong uniqueness principle is proved for an Euler-Poisson system in the whole space, with initial data so that the strong solution exists. Some results on Riesz potentials are used to justify the considered weak…

We analyze the Ericksen-Leslie system equipped with the Oseen-Frank energy in three space dimensions. Recently, the author introduced the concept of measure-valued solutions to this system and showed the global existence of these…

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…

We establish some conditional uniqueness of weak solutions to the viscous primitive equations, and as an application, we prove the global existence and uniqueness of weak solutions, with the initial data taken as small $L^\infty$…

We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity measuring kinetic energy cascade will also…

Contrary to the incompressible case not every measure-valued solution of the compressible Euler equations can be generated by weak solutions or a vanishing viscosity sequence. In the present paper we give sufficient conditions on an…