Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Hao Jia,Department of Mathematics University of Chicago
Inviter:
Scale invariant solutions to Navier Stokes equation and implications to Leray-Hopf weak solutions
Title:
数学所
Time & Venue:
2014.7.30 4:00pm N818
Abstract:
In this talk, I will first discuss the existence of scale invariant solutions to Navier Stokes equation with arbitrary ?1 homogeneous initial data. Since these solutions may not be small, linearized analysis seem to suggest nontrivial bifurcations. Under a quite plausible spectral assumption, we show rigorously that such bifurcations do occur and they imply non-uniqueness of scale-invariant solutions. By appropriately localizing such solutions, we then obtain non-uniqueness of Leray-Hopf weak solutions with initial data which are compactly supported, smooth away from origin, and having a singularity at the origin of the type $O(\frac{1}{|x|})$, which will be sharp. The verification of the spectral assumption involves only smooth and decaying functions, and seems to be doable numerically. This is joint work with V.Sverak.
Affiliation:
Appendix：
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