The self-similar solutions to full compressible Navier-Stokes equations without heat conductivity

In this work, we establish a class of globally defined large solutions to the free boundary problem of compressible full Navier{Stokes equations with constant shear viscosity, vanishing bulk viscosity and heat conductivity. We establish such solutions with initial data perturbed around the self-similar solutions when gamma > 7/6. In the case when 7/6 < gamma < 7/3, solutions 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 < gamma < 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. Our result extends the one of Hadzic and Jang [Expanding large global solutions of the equations of compressible fluid mechanics, J. Invent. Math. 214 (2018) 1205.] from the isentropic inviscid case to the non-isentropic viscous case.