2012/11/20 by Boris Haspot, Haspot, Boris
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1211.4819
openalex publication_date 2012/11/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
This paper is dedicated to the study of viscous compressible barotropic\nfluids in dimension N=2. We address the question of the global existence of\nstrong solutions with large initial data for compressible Navier-Stokes system\nand Korteweg system. In the first case we are interested by slightly extending\na famous result due to V. A. Vaigant and A. V. Kazhikhov in citeVG\nconcerning the existence of global strong solution in dimension two for a\nsuitable choice of viscosity coefficient (\μ(\ρ)=\μ>0 and\n\λ(\ρ)=\λ\ρ\β with \β>3) in the torus. We are going\nto weaken the condition on \β by assuming only \β>2 essentially by\ntaking profit of commutator estimates introduced by Coifman et al in cite4M\nand using a notion of \effective velocity as in citeVG. In the\nsecond case we study the existence of global strong solution with large initial\ndata in the sense of the scaling of the equations for Korteweg system with\ndegenerate viscosity coefficient and with friction term.\n