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제목 Singularity formation for the 3D axisymmetric Euler equations
발표자 정인지 ( KIAS ) 날짜 2018-03-06
Host KAIST Place 산업경영동(E2) 3221호
Abstract 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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