论文标题
不均匀抛物线方程和半空间中的Navier-Stokes方程的时间分析性
Time analyticity for inhomogeneous parabolic equations and the Navier-Stokes equations in the half space
论文作者
论文摘要
我们证明了在半空间中具有可测量系数的不均匀抛物线方程的弱解的时间分析性，在dirichlet边界条件或综合边界条件下，溶液和源术语具有相对于空间变量的订单$ 2 $的指数增长。我们还获得了半空间中不可压缩的Navier-Stokes方程的有界轻度解的时间分析性，并具有DIRICHLET边界条件。我们的工作是张[Proc。阿米尔。数学。 Soc。 148（2020）]和东张[J.功能。肛门。 （2020）]，作者证明了对均匀热方程和整个空间中Navier-Stokes方程的解决方案的时间分析。
We prove the time analyticity for weak solutions of inhomogeneous parabolic equations with measurable coefficients in the half space with either the Dirichlet boundary condition or the conormal boundary condition under the assumption that the solution and the source term have the exponential growth of order $2$ with respect to the space variables. We also obtain the time analyticity for bounded mild solutions of the incompressible Navier-Stokes equations in the half space with the Dirichlet boundary condition. Our work is an extension of the recent work by Zhang [Proc. Amer. Math. Soc. 148 (2020)] and Dong-Zhang [J. Funct. Anal. (2020)], where the authors proved the time analyticity of solutions to the homogeneous heat equation and the Navier-Stokes equations in the whole space.
