相关论文: On contact discontinuities in multi-dimensional is…

In this paper, we shall study the existence of weak solutions to Hessian type equations on compact Riemannian manifolds without boundary.

We study the incompressible Euler equation and prove that the set of weak solutions is path-connected. More precisely, we construct paths of H\"older regularity $C^{1/2}$, valued in $C^0_{t, loc} L^2_x$ endowed with the strong topology. The…

We prove the stability of contact discontinuities without shear, a family of special discontinuous solutions for the three-dimensional full Euler systems, in the class of vanishing dissipation limits of the corresponding…

We are concerned with the isothermal limit of entropy solutions in $L^\infty$, containing the vacuum states, of the Euler equations for isentropic gas dynamics. We prove that the entropy solutions in $L^\infty$ of the isentropic Euler…

We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…

We consider weak stationary solutions to the incompressible Euler equations and show that the analogue of the h-principle obtained in [5, 7] for time-dependent weak solutions continues to hold. The key difference arises in dimension d = 2,…

We consider the zero dissipation limit of the full compressible Navier-Stokes equations with Riemann initial data in the case of superposition of two rarefaction waves and a contact discontinuity. It is proved that for any suitably small…

This note aims at the following problem. In an ideal density dependent fluid system, is the total energy dissipated on shock type discontinuities? To this end, we study the local energy balance for weak solutions to the isentropic…

The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although…

This paper establishes the global existence of smooth solutions to the 2D isentropic and irrotational Euler equations for Chaplygin gases with a general class of short pulse initial data, which, in particular, resolves in this special case,…

We construct new stationary weak solutions of the 3D Euler equation with compact support. The solutions, which are piecewise smooth and discontinuous across a surface, are axisymmetric with swirl. The range of solutions we find is different…

This is the second paper in a series studying the nonlinear stability of rarefaction waves in multi-dimensional gas dynamics. We construct initial data near singularities in the rarefaction wave region and, combined with the a priori energy…

In this note, we establish Yudovich's existence and uniqueness result for bounded (as well as mildly unbounded) vorticity weak solution of the two-dimensional incompressible Euler equations. As a biproduct of our proof, we establish some…

We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreover, we establish existence of bounded weak solutions when…

We prove the existence of contact discontinuities for axisymmetric subsonic Euler flows with non-zero vorticity and non-zero angular momentum density in three-dimensional infinitely long cylinders. The problem is formulated as a two-phase…

We develop the theory of Riemann-Hilbert problems necessary for the results in part one of this series of papers. In particular, we obtain solutions for a family of non-linear Riemann-Hilbert problems through classical contraction…

We consider a simple nonlinear hyperbolic system modeling the flow of an inviscid fluid. The model includes as state variable the mass density fraction of the vapor in the fluid and then phase transitions can be taken into consideration;…

In this article we consider the discretely self-similar singular solutions of the Euler equations, and the possible velocity profiles concerned not only have decaying spatial asymptotics, but also have unconventional non-decaying…

In this paper, we study the regularity properties of bounded entropy solutions to the isentropic Euler equations with $\gamma = 3$. First, we use a blow-up technique to obtain a new trace theorem for all such solutions. Second, we use a…

In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total…