2021/09/16 by Cosmin Burtea, Cosmin, Burtea, Timothée Crin-Barat +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2109.07746
openalex publication_date 2021/09/16 · openalex created_date 2021/09/27 · openalex updated_date 2026/07/28
In this paper we study a singular limit problem in the context of partially\ndissipative first order quasilinear systems. This problem arises in multiphase\nfluid mechanics. More precisely, taking into account dissipative effects for\nthe velocity, we show that the so-called Kapilla system is obtained as a\nrelaxation limit from the Baer-Nunziato (BN) system and derive the convergence\nrate of this process. The main problem we encounter is that the (BN)-system\ndoes not verify the celebrated (SK) condition due to Shizuta and Kawashima. It\nturns out that we can rewrite the (BN)-system in terms of new variables such as\nto highlight a subsystem for which the linearized does verify the (SK)\ncondition which is coupled through lower-order terms with a transport equation.\nWe construct an appropriate weighted energy-functional which allows us to\ntackle the lack of symmetry of the system, provides decay information and\nallows us to close the estimate uniformly with respect to the relaxation\nparameter.\n