研究期間：10204~10307;In this project, we consider the well-posedness of a variety of models of mathematical fluid dynamics, and try to apply harmonic analysis methods to this class of problems. We will investigate the following interesting topics: In the first year, 1. Classical solution to the 2D generalized Benjamin-Bona-Mahony equation on upper half plane. 2. Critical thresholds in Euler-Poisson equations with pressure in spherical symmetric space-time. In the second year, 3. Local well-posedness of the compressible Navier-Stokes equations with density dependent viscosity in physical vacuum. 4. The global existence of weak solution to the shallow water equations.
