Global well posedness for the ghost effect system | Zendy

Bilal Al Taki | Zendy

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Global well posedness for the ghost effect system

Author(s) -

Bilal Al Taki

Publication year - 2016

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2017017

Subject(s) - degenerate energy levels , mach number , key (lock) , mathematics , inequality , compressibility , mathematical analysis , physics , computer science , quantum mechanics , computer security , mechanics , thermodynamics

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. JUNGEL, 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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