Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation

DOI10.1080/03605300500358152zbMath1158.76305OpenAlexW2132608559MaRDI QIDQ5291769

Xinwei Yu, Jian Deng, Thomas Yizhao Hou

Publication date: 22 May 2006

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300500358152

zbMATH Keywords

geometric propertiesglobal existencefinite time blowup3D Euler equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) First-order nonlinear hyperbolic equations (35L60) Initial value problems for first-order hyperbolic systems (35L45) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

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Cites Work

• Unnamed Item
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Singularity formation for complex solutions of the 3D incompressible Euler equations
• Groups of diffeomorphisms and the motion of an incompressible fluid
• On a new scale of regularity spaces with applications to Euler's equations
• 3D Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity
• Evidence for a singularity of the three-dimensional, incompressible Euler equations
• Cover illustration: vortex structure of Euler collapse
• Geometric Properties and Nonblowup of 3D Incompressible Euler Flow
• Geometric constraints on potentially
• Limiting case of the Sobolev inequality in BMO, with application to the Euler equations
• On the collapse of tubes carried by 3D incompressible flows