2022/02/04 by Gui‐Qiang Chen, Chen, Gui-Qiang G., Feimin Huang +3
Engineering · Mathematics · #35B30 #35B40 #35D30 #35L65 #35Q31 #76N15 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2202.02235
openalex publication_date 2022/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are concerned with the isothermal limit of entropy solutions in L^∞, containing the vacuum states, of the Euler equations for isentropic gas dynamics. We prove that the entropy solutions in L^∞ of the isentropic Euler equations converge strongly to the corresponding entropy solutions of the isothermal Euler equations, when the adiabatic exponent γ→ 1. This is achieved by combining careful entropy analysis and refined kinetic formulation with compensated compactness argument to obtain the required uniform estimates for the limit. The entropy analysis involves careful estimates for the relation between the corresponding entropy pairs for the isentropic and isothermal Euler equations when the adiabatic exponent γ→ 1. The kinetic formulation for the entropy solutions of the isentropic Euler equations with the uniformly bounded initial data is refined, so that the total variation of the dissipation measures in the formulation is locally uniformly bounded with respect to γ>1. The explicit asymptotic analysis of the Riemann solutions containing the vacuum states is also presented.