Seminar| Institute of Mathematical Sciences
Time: Friday, May 31th, 2024 , 14:30-15:30
Location：IMS, RS408
Speaker: Zirong Zeng, Nanjing University of Aeronautics and Astronautics
Abstract: In this talk, I will present our work concerning the 3D hyperdissipative Navier-Stokes equations on the torus. It is well-known that, due to Lions, for any L^2 divergence -free initial data, there exist a unique smooth Leray-Hopf solution when viscosity exponent is larger than 5/4. We proved that even in this high dissipative regime, the uniqueness would fail in the supercritical spaces in view of the LPS criteria. Moreover, the constructed solutions are allowed to coincide with the unique Leray-Hopf solutions near the initial time and, more delicately, admit the partial regularity outside a fractal set of singular times.