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\(L^p\)-theory for the time dependent Navier-Stokes problem with Navier-type boundary conditions. 2nd edition. (English) Zbl 1351.35100

Ahusborde, É. (ed.) et al., Thirteenth international conference Zaragoza-Pau on mathematics and its applications. Proceedings of the conference, Jaca, Spain, September 17–18, 2014. Zaragoza: Prensas de la Universidad de Zaragoza (ISBN 978-84-16515-68-4/pbk). Monografías Matemáticas “García de Galdeano” 40, 1-8 (2016).
Summary: We study the time dependent Navier-Stokes problem with Navier-type boundary conditions in \(L^p\)-spaces using semi-group theory. Proceeding as in [Y. Giga, J. Differ. Equations 61, 186–212 (1986; Zbl 0577.35058)] we prove the existence of a unique local in time mild solution to the Navier-Stokes problem with Navier-type boundaly conditions. Then proceeding as in [Y. Giga and T. Miyakawa, Arch. Ration. Mech. Anal. 89, 267–281 (1985; Zbl 0587.35078)] we prove that this solution is a classical one.
For the entire collection see [Zbl 1344.00012].

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
35K20 Initial-boundary value problems for second-order parabolic equations
35A20 Analyticity in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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