Blowup for model equations of fluid mechanics
Blowup for model equations of fluid mechanics
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Vu Hoang , Rice University
In this talk, I discuss recent progress towards proving a finite timeÌýblowup forÌýthe 2D inviscid Boussinesq equations, inspired by the hyperbolic flowÌýscenario.I will introduce various model equations for the Boussinesq systemÌýthat isolateÌýand capture possible mechanisms for singularity formation. AnÌýimportant theme is toÌýachieve finite-time blowup in a controlled manner. In the second partÌýof my talk,ÌýI describe a one-dimensional problem, which has singular solutionsÌýconverging to aÌýwell-defined profile at the time of blowup. ÌýThis talk is based on joint work with B. Orcan-Ekmecki, M. Radosz, andÌýH. Yang.Ìý