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Suitable Weak Solutions (suitable + weak_solution)

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Mathematics and Statistics100%

Selected Abstracts

On the number of singular points of weak solutions to the Navier-Stokes equations

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2001
Gregory A. Seregin
We consider a suitable weak solution to the three-dimensional Navier-Stokes equations in the space-time cylinder , × ]0, T[. Let , be the set of singular points for this solution and , (t) , {(x, t) , ,}. For a given open subset , , , and for a given moment of time t ,]0, T[, we obtain an upper bound for the number of points of the set ,(t) , ,. © 2001 John Wiley & Sons, Inc. [source]

Interior regularity criterion via pressure on weak solutions to the Navier,Stokes equations

MATHEMATISCHE NACHRICHTEN, Issue 1-2 2007
Tomoyuki Suzuki
Abstract Consider the nonstationary Navier,Stokes equations in , × (0, T), where , is a bounded domain in ,3. We prove interior regularity for suitable weak solutions under some condition on the pressure in the class of scaling invariance. The notion of suitable weak solutions makes it possible to obtain better information around the singularities. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A fully discrete nonlinear Galerkin method for the 3D Navier,Stokes equations

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2008
J.-L. Guermond
Abstract The purpose of this paper is twofold: (i) We show that the Fourier-based Nonlinear Galerkin Method (NLGM) constructs suitable weak solutions to the periodic Navier,Stokes equations in three space dimensions provided the large scale/small scale cutoff is appropriately chosen. (ii) If smoothness is assumed, NLGM always outperforms the Galerkin method by a factor equal to 1 in the convergence order of the H1 -norm for the velocity and the L2 -norm for the pressure. This is a purely linear superconvergence effect resulting from standard elliptic regularity and holds independently of the nature of the boundary conditions (whether periodicity or no-slip BC is enforced). © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source]

Existence and uniqueness of weak solutions for precipitation fronts: A novel hyperbolic free boundary problem in several space variables

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 10 2010
Andrew J. Majda
The determination of the large-scale boundaries between moist and dry regions is an important problem in contemporary meteorology. These phenomena have been addressed recently in a simplified tropical climate model through a novel hyperbolic free boundary formulation yielding three families (drying, slow moistening, and fast moistening) of precipitation fronts. The last two wave types violate Lax's shock inequalities yet are robustly realized. This formal hyperbolic free boundary problem is given here a rigorous mathematical basis by establishing the existence and uniqueness of suitable weak solutions arising in the zero relaxation limit. A new L2 -contraction estimate is also established at positive relaxation values. © 2010 Wiley Periodicals, Inc. [source]