About Schedule INS
现代分析与相关问题研讨会

Blowup of the entropy-bounded classical solutions to the nonisentropic compressible Navier-Stokes equations

Speaker

袁源 , 华南师范大学

Time

26 Mar, 17:05 - 17:45

Abstract

This talk concerns the instantaneous blowup of entropy-bounded classical solutions to the vacuum free boundary problem or the Cauchy problem of non-isentropic compressible Navier-Stokes equations. For vacuum free boundary problem, it is proved that with degenerate, temperature-dependent transport coefficients and prescribed decaying rate of the initial density across the vacuum boundary, (1) for three-dimensional spherically symmetric flows with non-vanishing bulk viscosity and zero heat conductivity, entropy-bounded classical solutions do not exist for any time, provided the initial velocity is expanding near the boundary; (2) for three-dimensional spherically symmetric flows with non-vanishing heat conductivity, the normal derivative of the temperature of the classical solution across the free boundary does not degenerate, and therefore the entropy immediately blowups if the decaying rate of the initial density does not satisfy the physical vacuum condition; For the one-dimensional Cauchy problem, it is proved that (3) with zero heat conduction and prescribed fast-decaying initial density profiles, entropy-bounded classical solutions do not exist for any time, provided the initial velocity or effective viscous flux is expanding at far field. These are joint works with Professor Zhouping XIN from the Chinese University of Hong Kong, Professor Jinkai LI from South China Normal University and Dr. Xin LIU from Texas A&M University.