Series:
PDE Seminar
Tuesday, February 12, 2019 - 3:00pm
1 hour (actually 50 minutes)
Location:
skiles 006
Organizer:
Abstract: In this talk, we consider the Cauchy problem of the N-dimensional
incompressible viscoelastic fluids with N ≥ 2. It is shown that, in the low frequency
part, this system possesses some dispersive properties derived from the one parameter
group e
±itΛ. Based on this dispersive effect, we construct global solutions with
large initial velocity concentrating on the low frequency part. Such kind of solution
has never been seen before in the literature even for the classical incompressible
Navier-Stokes equations. The proof relies heavily on the dispersive estimates for
the system of acoustics, and a careful study of the nonlinear terms. And we also
obtain the similar result for the isentropic compressible Navier-Stokes equations.
Here, the initial velocity with arbitrary B˙
N
2 −1
2,1
norm of potential part P
⊥u0 and
large highly oscillating are allowed in our results. (Joint works with Daoyuan Fang
and Ruizhao Zi)