On the convergence of quasilinear viscous approximations using compensated compactness and Kinetic Formulation

2022/09/04 by Ramesh Mondal, Mondal, Ramesh
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2209.01662

openalex publication_date 2022/09/04 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We use the method of Compensated Compactness and Kinteic Formulation to show that the almost everywhere limit of quasilinear viscous approximations is the unique entropy solution (in the sense of \it F. Otto) of the corresponding scalar conservation laws on a bounded domain in ℝ^d, where the viscous term is of the form ε div(B(u^ε)∇ u^ε).

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