Maximal Lp -Lq regularity to the Stokes problem with Navier boundary conditions

Author:

Al Baba Hind1

Affiliation:

1. Institute of Mathematics of the Czech Academy of Sciences , Z̆itná 25, 11567 Praha 1 , Czech Republic ; and Laboratoire de Mathématiques et de leurs applications Pau, UMR, CNRS 5142, Université de Pau et des pays de L’Adour, 64013 Pau cedex, France

Abstract

Abstract We prove in this paper some results on the complex and fractional powers of the Stokes operator with slip frictionless boundary conditions involving the stress tensor. This is fundamental and plays an important role in the associated parabolic problem and will be used to prove maximal L p L^{p} - L q L^{q} regularity results for the non-homogeneous Stokes problem.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Reference33 articles.

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2. H. Al Baba, C. Amrouche and M. Escobedo, Semi-group theory for the Stokes operator with Navier-type boundary conditions on L p L^{p} -spaces, Arch. Ration. Mech. Anal. 223 (2017), no. 2, 881–940.

3. H. Al Baba, C. Amrouche and A. Rejaiba, The time-dependent Stokes problem with Navier slip boundary conditions on L p L^{p} -spaces, Analysis (Berlin) 36 (2016), no. 4, 269–285.

4. H. Amann, Linear and Quasilinear Parabolic Problems. Vol. I: Abstract Linear Theory, Monogr. Math. 89, Birkhäuser, Boston, 1995.

5. Y. Amirat, D. Bresch, J. Lemoine and J. Simon, Effect of rugosity on a flow governed by stationary Navier–Stokes equations, Quart. Appl. Math. 59 (2001), no. 4, 769–785.

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