EXISTENCE OF WEAK SOLUTIONS FOR THE INCOMPRESSIBLE NONLINEAR PARABOLIC SYSTEM WITH DAMPING

  • Kabiru Michael Adeyemo Hallmark University Ijbebu-Itele, Ogun State
Keywords: Parabolic system, Existence, Damping, Weak solution

Abstract

This work concerns the existence of the weak solutions associated with the incompressible
 parabolic system with damping. The solution is shown to exist with data in Lesbegue space, L2.

References

X.J. Cai, Q.S. Jiu. Weak and strong solutions for the incompressible NavierStokes equations with damping. J. Math. Anal. Appl. 343 (2008) 799809.

E. Hopf. Uber die Anfangswertaufgabe fur die hydrodynamischen Grundgleichungen. Math. Nachr. vol. 4 (1951) pages 213-231

W. H. Karol and J. C. Robinson. Energy equality for the 3D critical convective Brinkman Forchheimer quations. arXiv:1612.02020v3 (2017) [math.AP].

V. Kalantarov, S. Zelik. Smooth attractors for the BrinkmanForchheimer equations with fast growing nonlinearities. Commun. Pure Appl. Anal. 11(2012), pages 20372054..

J. Leray. Sur le mouvement´dun liquide visqueux emplissant ´despace. Acta Math. vol. 63 (1934) pages 193248..

Petr Plechac and Vladimr Sverak. Singular and regular solutions of a non-linear parabolic system. J. of Nonlinearity, arXiv:math/0302129v1 [math.AP] 11 Feb 2003.

M. Struwe. On partial regularity results for the NavierStokes equations. Comm. Pure Appl. Math. 41 (1988) 437458.

M. Rockner, X. Zhang. Tamed 3D NavierStokes equation: existence, uniqueness and regularity.. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12, 4 (2009) pages 525549.

Z. Zhang, Xinglong Wu, Ming Lu. On the uniqueness of strong solutions to incompressible Navier-Stokes equation. J. Math. Anal. 377 (2011) 414-419.

Published
2023-04-13
How to Cite
Adeyemo, K. M. (2023). EXISTENCE OF WEAK SOLUTIONS FOR THE INCOMPRESSIBLE NONLINEAR PARABOLIC SYSTEM WITH DAMPING. Unilag Journal of Mathematics and Applications, 2(1), 1 - 8. Retrieved from http://lagjma.unilag.edu.ng/article/view/1372
Section
Articles