In this dissertation, we research some issues around the Navier-Stokes equations and Boltzmann- Enskog equation that are inside the active research section of applied math concepts. The device of Navier-Stokes equations is a typical instance of the conservation laws. While in the first area of the thesis, we study the world existence and convergence rates of methods to the three-dimensional compressible Navier-Stokes equations without heat conductivity. The rate is dissipative due to the viscosity, whereas the entropy is non-dissipative because of the lack of heat conductivity. The worldwide option is obtained by combining any local existence plus a priori estimates if H3-norm of this initial perturbation around a consistent state is sufficiently small and it is L1-norm is bounded….
Contents: Some problems on Navier-Stokes equations and Boltzmann equations
1 Global Existence and Convergence Rates for the 3-D Compressible Navier-Stokes Equations Without Heat Conductivity 1
1.1 Introduction
1.2 Reformulated system
1.3 Elementary
1.4 A priori estimates
1.5 Global existence and convergence rate
2 Existence of Nonlinear Boundary Layers to the Boltzamnn-Enskog Equa-tion for the CaseM∞ < −1
2.1 Introduction
2.1.1 Reformulation of half-space problem
2.1.2 Boltzmann collision operator
2.1.3 Boltzmann-Enskog equation
2.2 Nonlinear boundary layers for the caseM∞ < −1
2.2.1 Main result and estimates on the linear operator
2.2.2 Linear existence
2.2.3 Nonlinear existence
Bibliography
Some problems on Navier-Stokes equations and Boltzmann equations
Source: City University of Hong Kong