Sharp non-uniqueness for the 3D hyperdissipative Navier-Stokes equations: above the Lions exponent

发布时间：2022-11-09 作者：浏览次数：

Speaker:	曲鹏	DateTime:	2022年11月16日（星期三）上午9:30—10:30
Brief Introduction to Speaker: 曲鹏，复旦大学数学科学学院教授。主要从事应用偏微分方程的数学研究，在双曲守恒律、流体力学方程弱解等方面取得的成果曾发表在 Adv. Math., Arch. Rational Mech. Anal., J. Math. Pures Appl. 等国际知名期刊。曾获中国数学会钟家庆数学奖、中国工业与应用数学学会优秀青年学者奖。		Place:	腾讯会议：254-456-764
Abstract:In this talk, we would like to discuss 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 unique smooth Leray-Hopf solutions when the viscosity exponent is larger than 5/4. We prove that even in this high dissipative regime, the uniqueness would fail in the supercritical spaces in view of the generalized Ladyzenskaja-Prodi-Serrin condition. This talk is based on the joint work with Prof. Yachun Li, Prof. Deng Zhang and Dr. Zirong Zeng.