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Maximal $L_p$-$L_q$ regularity for the Stokes equations with various boundary conditions in the half space
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abstract
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.
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Cited by 1 Pith paper
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Regularity and Decay for Navier-Slip Fluid-Structure Interaction in Exterior Domains
For the linearized fluid-rigid body system with Navier-slip friction in an exterior domain, the associated operator has maximal L^q regularity, generates a bounded analytic semigroup, and obeys L^r–L^q decay estimates.
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