Naoto Kajiwara
Published 2022-01-14, updated 2022-04-29Version 2
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.
Poisson kernel and blow-up of the second derivatives near the boundary for Stokes equations with Navier boundary condition
Asymptotic stability of wave patterns to compressible viscous and heat-conducting gases in the half space
On elliptic equations in a half space or in convex wedges with irregular coefficients
![QR code for arXiv:2201.05306 [math.AP]](http://oss.arxitics.com/images/favicon.svg)