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Title: Green's Function for Viscous System
Keywords: Green's function, Compressible Navier-Stokes equation, Viscous Hyperbolic system, Long-Short wave decomposition, Weighted energy estimate
Issue Date: 15-Oct-2014
Source: WANG HAITAO (2014-10-15). Green's Function for Viscous System. ScholarBank@NUS Repository.
Abstract: In this thesis, we aim at developing the Algebraic Complex Scheme and applying it to study the Green?s function for viscous system. To be more specific, firstly 2 toy models, the 1-D convection heat equation and 1D compressible Navier-Stokes equation with Robin condition were investigated. The explicit full boundary data and the detailed quantitative description were obtained up to exponentially decaying terms. Next, we considered the multi-dimensional compressible Navier-Stokes equation in half space. We first obtained the point-wise estimates of fundamental solution for Cauchy problem by long-short wave decomposition and weighted energy estimate. Then we applied Liu-Yu algorithm to find the Green?s function in transformed variable. By comparing representation of fundamental solution and Green?s function in transformed variables, we obtained the Green?s function exactly in terms of composition of fundamental solution, heat kernel and their derivatives.
Appears in Collections:Ph.D Theses (Open)

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