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March 5, 2018 | 2:45 p.m. - 4:00 p.m.
Category: Lecture
Location: Education, College of #179 | Map
5425 Gullen Mall
Detroit, MI 48202
Cost: Free

Speaker:  Qi Zhang, University of California at Riverside

Title: Some recent results on axially symmetric Navier-Stokes equations

Abstract: For the three dimensional incompressible Navier-Stokes
equations (3dNS), there are two questions whose solution seems to be
beyond reach so far. One is whether Leray-Hopf weak solutions are
regular and the other is whether homogeneous D-solutions is zero. One
reason perhaps is that they are supercritical questions, which means
that known a priori  bound, say L^{10/3}_{loc}, is much weaker than
regularity criteria L^5_{loc}, e.g..  The axially
symmetric Navier-Stokes equations (ASNS) is a special case of 3d NS in
that the data is independent the longitudinal angle. Until recently it
was also regarded as a supercritical system. In this talk we survey
recent results showing that ASNS is essentially a critical system.
Although the regularity question is still far from being solved, it
seems to be encouraging psychologically. It is also shown that axially
symmetric D-solutions in a slab with a suitable boundary condition is
zero without extra smallness or decay conditions. Part of the results
is a joint work with Zhen Lei and others.


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