Global-in-Time solutions to equations of compressible fluid mechanics

Abstract

The Euler, and Euler-Poisson equations are famous in the fields of fluid mechanics and astrophysics as systems of nonlinear partial differential equations describing inviscid fluid flow. The basic equations were formulated by Euler in the 1750s. To this day, they are objects of much interest, with the fundamental questions of long-time behaviour, blow-up, and stability of solutions being active areas of research.
Recently, a large class of solutions to the compressible Euler equations was discovered by Sideris , achieved by reducing the problem to that of solving a system of nonlinear ODEs. In this thesis, we show that one need not rely on such a reduction by exhibiting a large family of expanding, global-in-time solutions to the free boundary compressible Euler equations that instead take advantage of scaling mechanisms inherent to the system. We then adapt this technique to find expanding solutions of the free boundary compressible Euler-Poisson, and N-body Euler-Poisson systems.

Date of Award	1 Apr 2021
Original language	English
Awarding Institution	King's College London
Supervisor	Alexander Pushnitski (Supervisor) & Mahir Hadzic (Supervisor)