A Level Set Formulation for the 3D Incompressible Euler Equations
نویسندگان
چکیده
منابع مشابه
A Level Set Formulation for the 3d Incompressible Euler Equations
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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where ν is the unit exterior normal to ∂D. If v = (v, . . . , v) : [0, T ] ×D → R, then (adopting the summation convention) div v = ∂jv is the spatial divergence of v, ∇v is the spatial gradient, and ( v · ∇ ) v is the vector in R whose i-th component is given by v∂jv . Hence, (1.1) is a system of (d + 1) equations for the (d + 1) unknowns (v, . . . , v, p), where p : [0, T ] ×D → R physically ...
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We 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 vel...
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ژورنال
عنوان ژورنال: Methods and Applications of Analysis
سال: 2005
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.2005.v12.n4.a4