Local strong solutions of the three-dimensional Stokes approximation equations
Guo Zhen-hua · Journal of Northwest University · 2011
Aim In order to study the existence,uniqueness,stability of the local strong solutions of the three-dimensional Stokes approximation equations in a bounded smooth domain.Methods The approximate solutions have been constructed via a semi-discrete Galerkin scheme,using uniform estimates and solutions have been obtained by passing to the limit.Results Provided that the initial data satisfies a natural compatibility condition,the initial density needs not be bounded away from zero.Namely,the initial density may vanish in an open subset of Ω,and then the three-dimensional Stokes approximation equations have a local strong solution.Conclusion The existence,uniqueness,stability of the local strong solutions is proved.