Add to ORKGWe study a 1D model for the 3D incompressible Euler equations in axisymmetric geometries, which can be viewed as a local approximation to the Euler equations near the solid boundary of a cylindrical domain. We prove the local well-posedness of the model in spaces of zero-mean functions, and study the potential formation of a finite-time singularity under certain convexity conditions for the velocity field. It is hoped that the results obtained on the 1D model will be useful in the analysis of the full 3D problem, whose loss of regularity in finite time has been observed in a recent numerical study (Luo and Hou, 2013)
In connection with the recent proposal for possible singularity formation at the boundary for soluti...
In connection with the recent proposal for possible singularity formation at the boundary for soluti...
In this paper, we present strong numerical evidences that the incompressible axisymmetric Euler equa...
We study a 1D model for the 3D incompressible Euler equations in axisymmetric geometries, which can...
In connection with the recent proposal for possible singularity formation at the boundary for soluti...
In connection with the recent proposal for possible singularity formation at the boundary for soluti...
Whether the three-dimensional incompressible Euler equations can develop a singularity in finite tim...
Whether the three-dimensional incompressible Euler equations can develop a singularity in finite tim...
Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth init...
In (Comm Pure Appl Math 62(4):502–564, 2009), Hou and Lei proposed a 3D model for the axisymmetric i...
We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, w...
The question of finite-time blowup of the 3D incompressible Euler equations is numerically investiga...
Inspired by the recent numerical evidence of a potential 3D Euler singularity [28, 29], we prove the...
Inspired by the numerical evidence of a potential 3D Euler singularity by Luo-Hou [30,31] and the re...
Whether the three-dimensional (3D) incompressible Euler equations can develop a finite-time singular...
In connection with the recent proposal for possible singularity formation at the boundary for soluti...
In connection with the recent proposal for possible singularity formation at the boundary for soluti...
In this paper, we present strong numerical evidences that the incompressible axisymmetric Euler equa...
We study a 1D model for the 3D incompressible Euler equations in axisymmetric geometries, which can...
In connection with the recent proposal for possible singularity formation at the boundary for soluti...
In connection with the recent proposal for possible singularity formation at the boundary for soluti...
Whether the three-dimensional incompressible Euler equations can develop a singularity in finite tim...
Whether the three-dimensional incompressible Euler equations can develop a singularity in finite tim...
Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth init...
In (Comm Pure Appl Math 62(4):502–564, 2009), Hou and Lei proposed a 3D model for the axisymmetric i...
We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, w...
The question of finite-time blowup of the 3D incompressible Euler equations is numerically investiga...
Inspired by the recent numerical evidence of a potential 3D Euler singularity [28, 29], we prove the...
Inspired by the numerical evidence of a potential 3D Euler singularity by Luo-Hou [30,31] and the re...
Whether the three-dimensional (3D) incompressible Euler equations can develop a finite-time singular...
In connection with the recent proposal for possible singularity formation at the boundary for soluti...
In connection with the recent proposal for possible singularity formation at the boundary for soluti...
In this paper, we present strong numerical evidences that the incompressible axisymmetric Euler equa...