袁源副研究员，华南师范大学

This talk concerns the instantaneous blowup of entropy-bounded classical solutions to the vacuum free boundary problem or the Cauchy problem of nonisentropic compressible Navier-Stokes equations.

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 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;

Cauchy problem: we also have similar results for the one-dimensional flows with zero heat conduction and prescribed fast-decaying initial density profiles.

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.