Some problems on a class of fluid dynamical systems

In this MPhil thesis, we consider the solutions for a class of fluid dynamical systems, such as the isentropic Euler-Poisson, Navier-Stokes-Poisson, Navier-Stokes, Euler systems. As these systems share some similar mathematical structures, we would like to find the relationship between them, such as some blowup and stability phenomena…


1 Introduction
2 Blowup Solutions I
2.1 Blowup Solutions
2.2 2-dimensional Isothermal Fluids
2.3 Blowup Rates
3 Blowup Solutions II
3.1 Systems with Potential Forces
3.2 Systems without Potential Forces
4 Non-global Existence
4.1 Non-global Existence of Isothermal Tame Solutions
4.2 Energy of the Solutions
4.3 Euler-Poisson Equations
4.4 Euler-Poisson Equations with Frictional Damping
5 Discussion
5.1 Explicit Stationary Solutions
5.2 Blowup Solutions
5.3 Tame Solutions
5.4 Stability of Stationary Solutions

Author: Yuen, Manwai

Source: City University of Hong Kong

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