讲座内容：

This talk is concerned with the Cauchy problem of compressible viscous and diffusive Oldroyd-B model for viscoelastic fluids, which can be formally derived from the compressible Navier-Stokes-Fokker-Planck system via the micro-macro analysis. For the 3D equations with constant transport coefficients, we first prove the global existence and large-time behavior of “intermediate weak” solutions with discontinuous and low-energy data, which may have large oscillations and contain vacuum. It is shown that the global weak solution becomes a strong one, provided the initial data is more regular. For the 2D equations, the global well-posedness of strong solutions with large data is established, provided the volume (bulk) viscosity depends on the density in a specific form.