Friday, March 2, 2018

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2018-03-08 / 16:00 ~ 18:00
세미나 - PDE 세미나: 인쇄
by 정인지()

We consider the 3D axisymmetric Euler equations on exterior domains $ { (x,y,z) : (1 + epsilon |z|)^2 le x^2 + y^2 } $ for any $epsilon > 0$ so that we can get arbitrarily close to the exterior of a cylinder. We construct a strong local well-posedness class, and show that within this class there exist compactly supported initial data which blows up in finite time. The local well-posedness class consists of velocities which are uniformly Lipschitz in space and have finite energy. Our results were inspired by recent works of Hou-Luo, Kiselev-Sverak, and many others, and the proof builds up on our previous works on 2D Euler and Boussinesq systems. This is joint work with Tarek Elgindi. 


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