2018/11/05 by Xin Liu, Yuan Yuan, Liu, Xin +1
Engineering · Mathematics · #35A01 #35A09 #35B40 #76N10 #76N15 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1811.01810
openalex publication_date 2018/11/05 · openalex created_date 2018/11/09 · openalex updated_date 2026/07/28
In this work, we establish a class of globally defined, large solutions to the free boundary problem of compressible Navier-Stokes equations with constant shear viscosity and vanishing bulk viscosity. We establish such solutions with initial data perturbed arbound any self-similar solution when γ> 7/6. In the case when 7/6 < γ< 7/3, as long as the self-similar solution has bounded entropy, a solution with bounded entropy can be constructed. It should be pointed out that the solutions we obtain in this fashion do not in general keep being a small perturbation of the self-similar solution due to the second law of thermodynamics, i.e., the growth of entropy. If in addition, in the case when 11/9 < γ< 5/3, we can construct a solution as a global-in-time small perturbation of the self-similar solution and the entropy is uniformly bounded in time.