Mathematical analysis of an incompressible viscous fluid in an infinite layer by methods of real analysis

分析了无限层上Stokes方程的一个预解问题，证明了Stokes算子在保持器和Besov空间上生成一个解析半群.作为应用，我们证明了Besov空间中某些特殊解的稳定性。利用算子值Fourier乘子定理证明了Stokes方程的极大正则性，并证明了Navier-Stokes方程自由边值问题局部时间解的唯一存在性.

We analyze a resolvent problem of the Stokes equation in an infinite layer and prove that the Stokes operator generates an analytic semigroup on Holder and Besov spaces. As an application, we prove a stability of some special solutions in Besov spaces. Moreover, we prove maximal regularity for the Stokes equation by operator-valued Fourier multiplier theorem, and we prove unique existence of a local in time solution to free boundary problems of the Navier-Stokes equation.