Weak solutions of Navier-Stokes equations
نویسندگان
چکیده
منابع مشابه
Lagrangian Approximations and Weak Solutions of the Navier-Stokes Equations
The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian re...
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We consider the Clay Institute Prize Problem asking for a mathematical analytical proof of existence, smoothness and uniqueness (or a converse) of solutions to the incompressible Navier-Stokes equations. We argue that the present formulation of the Prize Problem asking for a strong solution is not reasonable in the case of turbulent flow always occuring for higher Reynolds numbers, and we propo...
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The simplest, most elementary proofs of the existence of solutions of the Navier-Stokes equations are given via Galerkin approximation. The core of such proofs lies in obtaining estimates for the approximations from which one can infer their convergence (or at least the convergence of a subsequence of the approximations) as well as some degree of regularity of the resulting solution. The first ...
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driven by white noise Ẇ . Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navier–Stokes equation is proved. In the two-dimensional case, the existence and pathwise uniqueness of a global strong solution is shown. A Wiener chaosbased criterion for the existence and uniqueness of a strong global ...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1984
ISSN: 0040-8735
DOI: 10.2748/tmj/1178228767