2024/08/09 by Yachun Li, Peng Lu, Li, Yachun +5
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2408.05138
openalex publication_date 2024/08/09 · openalex created_date 2024/09/21 · openalex updated_date 2026/07/28
The purpose of this work is to investigate the Cauchy problem of global-in-time existence of large strong solutions to the Navier-Stokes equations for compressible viscous and heat conducting fluids. A class of density-dependent viscosity is considered. By introducing the modified effective viscous flux and using the bootstrap argument, we establish the global existence of large strong solution when the initial density is linearly equivalent to a large constant state. It is worthy of mentioning that, different from the work of Matsumura and Nishida (J. Math. Kyoto Univ., 1980) with small initial perturbation and the work of Huang and Li (Arch. Ration. Mech. Anal., 2018) with small energy but possibly large oscillations, our global large strong solution is uniform-in-time in H2 Sobolev space and the uniform-in-time bounds of both density and temperature are obtained without any restrictions on the size of initial velocity and initial temperature. In addition, when the initial data belongs to Lp0∩ H2 with p0∈[1,2], we establish the convergence of the solution to its associated equilibrium with an explicit decay rate whether the initial data close to or far away from the equilibrium in the whole space. As a result, we give a specific large strong solution in Sobolev space satisfying the global existence assumptions proposed by Villani (Mem. Amer. Math. Soc., 2009), He, Huang, and Wang (Arch. Ration. Mech. Anal., 2019), Zhang and Zi (Ann. Inst. H. Poincare Anal. Non Lineaire, 2020) in studying the asymptotic behavior of solution, and extend the second above result to the nonisentropic case. This paper considers for the first time the application of Fourier splitting method to Navier-Stokes equations with variable viscosity.