论文标题
最大$ l_p $ - $ l_q $适用于半空间中各种边界条件的stokes方程
Maximal $L_p$-$L_q$ regularity for the Stokes equations with various boundary conditions in the half space
论文作者
论文摘要
我们证明了分解$ l_p $估计和最大$ l_p $ - $ l_q $定期估计，用于半空间中的Dirichlet，Neumann和Robin边界条件的Stokes方程。每个解决方案均由$ x'$ - 方向的傅立叶乘数和$ x_n $ - 方向的积分构建。我们分解解决方案，使得傅立叶乘数的符号是有界和全态的。我们看到，操作员规范以$ -1 $的均质功能为主导，$ -1 $，$ x_n $ - 方向。基础是Weis的操作员值傅立叶乘数定理和内核操作员的界限。我们提供了一种新的简单方法，以在半空间中获得最大规律性。
We prove resolvent $L_p$ estimates and maximal $L_p$-$L_q$ regularity estimates for the Stokes equations with Dirichlet, Neumann and Robin boundary conditions in the half space. Each solution is constructed by a Fourier multiplier of $x'$-direction and an integral of $x_N$-direction. We decompose the solution such that the symbols of the Fourier multipliers are bounded and holomorphic. We see that the operator norms are dominated by a homogeneous function of order $-1$ for $x_N$-direction. The basis are Weis's operator-valued Fourier multiplier theorem and a boundedness of a kernel operator. We give a new simple approach to get maximal regularity in the half space.
