On the breakdown of axisymmetric smooth solutions for the 3-D Euler equations

DOI10.1007/BF02099454zbMath0858.76068MaRDI QIDQ1924026

Namkwon Kim, Donghao Chae

Publication date: 12 March 1997

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

cylindrical coordinatesaxial symmetryBeale-Kato-Majda criterionangular component of vorticityhigher Sobolev norms

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

Related Items

On strong convergence to 3D axisymmetric vortex sheets, Axisymmetric solutions to the 3D Euler equations, Decay rates of second order derivatives of axisymmetric \(D\)-solutions to the stationary Navier-Stokes equations, 2D inviscid heat conductive Boussinesq equations on a bounded domain, Instability for axisymmetric blow-up solutions to incompressible Euler equations, Viscous approximation and weak solutions of the 3D axisymmetric Euler equations, On the Lagrangian dynamics of the axisymmetric 3D Euler equations, Removing type II singularities off the axis for the three dimensional axisymmetric Euler equations, An unfinished tale of nonlinear PDEs: Do solutions of 3D incompressible Euler equations blow-up in finite time?, Generic solvability of the axisymmetric 3-D Euler equations and the 2-D Boussinesq equations

Cites Work

• Unnamed Item
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Nonstationary flows of viscous and ideal fluids in \(R^3\)
• Remarks on axisymmetric solutions of the incompressible euler system