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Regularity of solutions to the Navier-Stokes equations with a nonstandard boundary condition

Regularity of solutions to the Navier-Stokes equations with a nonstandard boundary condition In this paper we are concerned with the regularity of solutions to the Navier-Stokes equations with the condition on the pressure on parts of the boundary where there is flow. For the steady Stokes problem a result similar to L q -theory for the one with Dirichlet boundary condition is obtained. Using the result, for the steady Navier-Stokes equations we obtain regularity as the case of Dirichlet boundary conditions. Furthermore, for the time-dependent 2-D Navier-Stokes equations we prove uniqueness and existence of regular solutions, which is similar to J.M.Bernard’s results[6] for the time-dependent 2-D Stokes equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Regularity of solutions to the Navier-Stokes equations with a nonstandard boundary condition

Acta Mathematicae Applicatae Sinica , Volume 31 (3) – Jul 12, 2015

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-015-0497-x
Publisher site
See Article on Publisher Site

Abstract

In this paper we are concerned with the regularity of solutions to the Navier-Stokes equations with the condition on the pressure on parts of the boundary where there is flow. For the steady Stokes problem a result similar to L q -theory for the one with Dirichlet boundary condition is obtained. Using the result, for the steady Navier-Stokes equations we obtain regularity as the case of Dirichlet boundary conditions. Furthermore, for the time-dependent 2-D Navier-Stokes equations we prove uniqueness and existence of regular solutions, which is similar to J.M.Bernard’s results[6] for the time-dependent 2-D Stokes equations.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 12, 2015

References