On Strong Continuity of Weak Solutions to the Compressible Euler System

Weak and strong solutions of equations of compressible magnetohydrodynamics

Periodic Solutions of Compressible Euler

We have been working on a long term program to construct the first time-periodic solutions of the compressible Euler equations. Our program from the start has been to construct the simplest periodic wave structure, and then tailor the analysis in a rigorous existence proof to the explicit structure. In [26] have found the periodic structure, in [27, 28] we showed that linearized solutions with ...

Weak-strong uniqueness for the isentropic compressible Navier-Stokes system

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong uniqueness results are improved. Classical uniqueness results for this equation follow naturally.

Perturbational blowup solutions to the compressible Euler equations with damping

BACKGROUND The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. METHOD In this...

Global Solutions to the Compressible Euler Equations with Geometrical Structure

We prove the existence of global solutions to the Euler equations of compressible isentropic gas dynamics with geometrical structure, including transonic nozzle flow and spherically symmetric flow. Due to the presence of the geometrical source terms, the existence results themselves are new, especially as they pertain to radial flow in an unbounded region, |~x| ≥ 1, and to transonic nozzle flow...