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\(L_p\)-\(L_q\) maximal regularity of the Neumann problem for the Stokes equations in a bounded domain. (English) Zbl 1141.35344
Kozono, Hideo (ed.) et al., Asymptotic analysis and singularities. Hyperbolic and dispersive PDEs and fluid mechanics. Papers of the 14th International Research Institute of the Mathematical Society of Japan (MSJ), Sendai, Japan, July, 18–27, 2005. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-40-2/hbk). Advanced Studies in Pure Mathematics 47-1, 349-362 (2006).
Summary: We consider the Neumann problem for the Stokes equations with non-homogeneous boundary and divergence conditions in a bounded domain. We obtain a global in time \(L_p\)-\(L_q\) maximal regularity theorem with exponential stability. To prove the \(L_p\)-\(L_q\) maximal regularity, we use the Weis operator valued Fourier multiplier theorem.
For the entire collection see [Zbl 1130.35003].

35B45 A priori estimates in context of PDEs
35Q30 Navier-Stokes equations