Geometric Properties and Nonblowup of 3D Incompressible Euler Flow
نویسندگان
چکیده
منابع مشابه
Geometric Properties and Nonblowup of 3D Incompressible Euler Flow∗
has been one of the most outstanding open problems. It plays a very important role in understanding the core problems in hydrodynamics such as the onset of turbulence (people have also tried to understand turbulence through studying weak solutions; see Scheffer, 1993 or Shnirelman, 1997). Much effort has been made to answer this question; see, e.g., Beale et al. (1984), Ebin et al. (1970), Cafl...
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This is a follow-up of our recent article Deng et al. (2004). In Deng et al. (2004), we derive some local geometric conditions on vortex filaments which can prevent finite time blowup of the 3D incompressible Euler equation. In this article, we derive improved geometric conditions which can be applied to the scenario when velocity blows up at the same time as vorticity and the rate of blowup of...
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Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by presenting a class of potentially singular solutions to the Euler equations computed in ax...
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which implies that the topology of the vorticity vector field must be very simple. Even local existence of the Clebsch representation is only guaranteed at points where the vorticity does not vanish. It has been shown (Graham-Henyey [17]) that in general (1.3) can not hold around a point with zero vorticity. For more discussion on the properties of classical Clebsch variables and its various ge...
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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 ...
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ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2005
ISSN: 0360-5302,1532-4133
DOI: 10.1081/pde-200044488