$ L^p $-strong solution for the stationary exterior Stokes equations with Navier boundary condition-Reference-Cited by-同舟云学术

$ L^p $-strong solution for the stationary exterior Stokes equations with Navier boundary condition

Published:2022 Issue:6 Volume:15 Page:1403
ISSN:1937-1632
Container-title:Discrete and Continuous Dynamical Systems - S
language:
Short-container-title:DCDS-S

Author:

Dhifaoui Anis¹

Affiliation:

1. LR Analysis and Control of PDEs, LR22ES03, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Tunisia

Abstract

<p style='text-indent:20px;'>This paper treats the stationary Stokes problem in exterior domain of <inline-formula><tex-math id="M2">\begin{document}$ {{\mathbb{R}}}^3 $\end{document}</tex-math></inline-formula> with Navier slip boundary condition. The behavior at infinity of the data and the solution are determined by setting the problem in <inline-formula><tex-math id="M3">\begin{document}$ L^p $\end{document}</tex-math></inline-formula>-spaces, for <inline-formula><tex-math id="M4">\begin{document}$ p> 2 $\end{document}</tex-math></inline-formula>, with weights. The main results are the existence and uniqueness of strong solutions of the corresponding system.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference41 articles.

1. P. Acevedo, C. Amrouche, C. Conca, A. Ghosh.Stokes and Navier-Stokes equations with Navier boundary condition, C. R. Math. Acad. Sci. Paris, 357 (2019), 115-119.

2. Y. Achdou, O. Pironneau.Domain decomposition and wall laws, C. R. Acad. Sci. Paris Sér. I Math., 320 (1995), 541-547.

3. Y. Achdou, O. Pironneau, F. Valentin.Effective boundary conditions for laminar flows over periodic rough boundaries, J. Comput. Phys., 147 (1998), 187-218.

4. Y. Achdou, O. Pironneau and F. Valentin, Shape control versus boundary control, Équations aux Dérivées Partielles et Applications, Gauthier-Villars, Éd. Sci. Méd. Elsevier, Paris, (1998), 1–18.

5. F. Alliot, C. Amrouche.The Stokes problem in $\mathbb{R}^n$: An approach in weighted Sobolev spaces, Math. Models Methods Appl. Sci., 9 (1999), 723-754.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. One Navier’s problem for the Brinkman system;ANNALI DELL'UNIVERSITA' DI FERRARA;2023-02-25

2. Very weak solution for the stationary exterior Stokes equations with non‐standard boundary conditions in L ^p ‐theory;Mathematical Methods in the Applied Sciences;2022-07-07