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Abstract:
Despite the effort of mathematicians over generations ever since the pioneering work of Leray in 1930s, the Navier-Stokes problem, specifically whether a solution initiated from sufficiently smooth data preserves its regularity or experiences a finite-time blowup, remains unsolved. Nevertheless, very recently, remarkable progress has been made on various topics. For example, numerical analysis led to a wide range of toy models that have much similarity to the Navier-Stokes equations and yet display a finite-time blowup; harmonic analysis allowed us to obtain well-posedness and regularity criteria that are unthinkable with classical methods; stochastic analysis revealed interesting effect of random noise that may regularize the solution or potentially cause finite-time singularity. The following related equations have also attracted much attention from researchers: Euler equations, Boussinesq system, KdV equations, micropolar fluid system, hydrodynamics models such as magnetohydrodynamics system, geophysics models such as the surface quasi-geostrophic equations.
The purpose of this special session is to invite researchers devoted to analysis on fluid mechanics but possibly with different expertise and wide range of background and encourage deep discussions from unconventional approach.
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