منابع مشابه
Incompressible Euler Equations : the blow - up problem and related results
The question of spontaneous apparition of singularity in the 3D incompressible Euler equations is one of the most important and challenging open problems in mathematical fluid mechanics. In this survey article we review some of recent approaches to the problem. We first review Kato’s classical local well-posedness result in the Sobolev space and derive the celebrated Beale-Kato-Majda criterion ...
متن کاملFinite Time Blow-up for the 3D Incompressible Euler Equations
We prove the finite time blow-up for solutions of the 3D incompressible Euler equations, which happens along the fluid particle trajectories starting from a set of points. This set is specified by the relation between the deformation tensor and the Hessian of pressure both coupled with the vorticity directions, associated with the initial data. As a corollary of this result we prove the finite ...
متن کاملBlow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations
Whether the 3D incompressible Euler and Navier–Stokes equations can develop a finite-time singularity from smooth initial data with finite energy has been one of the most long-standing open questions. We review some recent theoretical and computational studies which show that there is a subtle dynamic depletion of nonlinear vortex stretching due to local geometric regularity of vortex filaments...
متن کاملFinite Time Blow-up of a 3D Model for Incompressible Euler Equations
We investigate the role of convection on its large time behavior of 3D incompressible Euler equations. In [15], we constructed a new 3D model by neglecting the convection term from the reformulated axisymmetric Navier-Stokes equations. This model preserves almost all the properties of the full Navier-Stokes equations, including an energy identity for smooth solutions. The numerical evidence pre...
متن کاملExact, infinite energy, blow-up solutions of the three-dimensional Euler equations
For the class of cylindrically symmetric velocity fields U(r, z, t) = {u(r, t), v(r, t), zγ (r, t)}, two infinite energy exact solutions of the three-dimensional incompressible Euler equations are exhibited that blow up at every point in space in finite time. The first solution is embedded within the second as a special case and in both cases v = 0. Both solutions represent three-dimensional vo...
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ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 2008
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-008-0184-x