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 in Dong and Zhang (Time analyticity for the heat equation and Navier–Stokes equations. arXiv:1907.01687 (to appear in J Funct Anal)) and Zhang (Proc Am Math Soc 148(4):1665–1670, 2020), where the authors proved the time analyticity of solutions to the homogeneous heat equation and the Navier–Stokes equations in the whole space.

中文翻译：

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半空间中非均质抛物方程和Navier-Stokes方程的时间解析

我们在Dirichlet边界条件或常态边界条件下，假设半解中具有可测量系数的非齐次抛物方程的弱解的时间解析性，并假设该解和源项相对于2阶呈指数增长空间变量。我们还获得了具有Dirichlet边界条件的半空间中不可压缩Navier-Stokes方程的有界温和解的时间解析性。我们的工作是对Dong和Zhang（热方程和Navier–Stokes方程的时间分析。arXiv：1907.01687（将在J Funct Anal中出现））和Zhang（Proc Am Math Soc 148（4）： 1665–1670，2020），