3D compressible viscoelastic flows with zero shear viscosity and general pressure law
Prof. ZHANG Ting
Date & Time
24 Oct 2025 (Fri) | 10:00 AM - 11:00 AM
Venue
Y5-305, YEUNG
ABSTRACT
In this talk, we study the three-dimensional compressible viscoelastic flows with zero shear viscosity and a general class of pressure laws. We do not need the monotonically increasing pressure law with the help of the elasticity coefficient θ of the fluid, only need the condition P′(1)+θ>0. We shall reformulate the systems with the new perturbation variables (ρ−1,u,F−ρ1I) and (ρ−1,u,F−I) to deal with the compressible and incompressible parts, separately. For the compressible parts, we shall use the vector field methods to derive the weighted energy decay. For the incompressible parts, a local energy decay will be applied to derive the weighted estimates. To overcome the difficulty of the lack of dissipation for the incompressible parts, we shall introduce ``good unknowns'', and use the implicit structure of the nonlinearities. With the help of vector fields, we derive the weighted L2 energy to prove global stability around a constant equilibrium.
