Small scales and singularity formation in fluid dynamics

Abstract

We review recent advances in understanding singularity and small scales formation in solutions of fluid dynamics equations. The focus is on the Euler and surface quasi-geostrophic (SQG) equations and associated models.

20 pages, Proceedings of ICM 2018

References in corpus (8)

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• Infinite superlinear growth of the gradient for the two-dimensional Euler equation
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• Finite-time Singularity formation for Strong Solutions to the axi-symmetric $3D$ Euler Equations
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• On the Effects of Advection and Vortex Stretching
• Blowup with vorticity control for a 2D model of the Boussinesq equations
• A Computational Investigation of the Finite-Time Blow-Up of the 3D Incompressible Euler Equations Based on the Voigt Regularization

Cited by in corpus (2)

• Finite time blowup of 2D Boussinesq and 3D Euler equations with $C^{1,\alpha }$ velocity and boundary
• The incompressible Euler equations under octahedral symmetry: singularity formation in a fundamental domain