报告方式：腾讯会议849-922-032
Abstract: Derived in 1820s, the Navier-Stokes equations (NSEs) govern the motion of fluid flows. In 1930s, Leray established the theory of weak solutions for the NSEs and raised some questions, many of which still remain open. One renowned question regards the appearance of singularity of weak solutions in finite time, which lies at the heart of the most exiting developments in fluid dynamics. The well-posedness problem, particularly in Leray-Hopf space, is also eminent and unanswered. The talk will review some major breakthroughs toward resolving the aforementioned problems. The emphasis will be on some recent groundbreaking work, sparked by empirical laws in physics and techniques from other fields in mathematics, in particular, the convex integration techniques. We will also discuss some ongoing interest in various problems and new perspectives opened up by these techniques.
