Global well posedness for the ghost effect system

Bilal Al Taki

doi:10.3934/cpaa.2017017

Article Contents

2017, Volume 16, Issue 1: 345-368. Doi: 10.3934/cpaa.2017017

This issue Previous Article Periodic solutions for nonlocal fractional equations Next Article Erratum: "On the nonlocal Cahn-Hilliard-Brinkman and Cahn-Hilliard-Hele-Shaw systems" [Comm. Pure Appl. Anal. 15 (2016), 299--317]

Global well posedness for the ghost effect system

Bilal Al Taki^1,2, ,

1.
LAMA, UMR 5127 CNRS, Université de Savoie Mont, Blanc 73376 Le Bourget du lac cedex, France
2.
Laboratory of Mathematics-EDST, Lebanese University, Beirut, Lebanon

E-mail address: bilal.al-taki@univ-smb.fr
E-mail address: bilal.al-taki@univ-smb.fr

Received: August 2016

Revised: September 2016

Published: January 2018

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Abstract

The aim of this paper is to discuss the issue of global existence of weak solutions of the so called ghost effect system which has been derived recently in [C. D. LEVERMORE, W. SUN, K. TRIVISA, SIAM J. Math. Anal. 2012]. We extend the local existence of solutions proved in [C.D. LEVERMORE, W. SUN, K. TRIVISA, Indiana Univ. J., 2011] to a global existence result. The key tool in this paper is a new functional inequality inspired of what proposed in [A. JÜNGEL, D. MATTHES, SIAM J. Math. Anal., 2008]. Such an inequality being adapted in [D. BRESCH, A. VASSEUR, C. YU, 2016] to be useful for compressible Navier-Stokes equations with degenerate viscosities. Our strategy to prove the global existence of solution builds upon the framework developed in [D. BRESCH, V. GIOVANGILI, E. ZATORSKA, J. Math. Pures Appl., 2015] for low Mach number system.

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Mathematics Subject Classification: 35G25, 35Q30, 35Q40, 35D30, 82D05, 82D37.

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References

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