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Research Activities > Programs > Incompressible Flows at High Reynolds Number > Tom Hou

Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number

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Geometric Properties and Non-blowup of 3-D Incompressible Euler Flow

Dr. Tom Hou

Applied and Computational Mathematics at California Institute of Technology

Abstract:   By exploring a local geometric property of the vorticity field along a vortex filament, we establish a sharp relationship between the geometric properties of the vorticity field and the maximum vortex stretching. This new understanding leads to an improved result of the global existence of the 3-D Euler equation under mild assumptions that are consistent with the observations from recent numerical computations. This is a joint work with Dr. Jian Deng and Mr. Xinwei Yu.