On the uniqueness of weak solutions for the 3D Navier-Stokes equations
Qionglei Chen, Changxing Miao, Zhifei Zhang (2009)
Annales de l'I.H.P. Analyse non linéaire
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Qionglei Chen, Changxing Miao, Zhifei Zhang (2009)
Annales de l'I.H.P. Analyse non linéaire
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Tetsuro Miyakawa, Maria Elena Schonbek (2001)
Mathematica Bohemica
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This paper is concerned with optimal lower bounds of decay rates for solutions to the Navier-Stokes equations in . Necessary and sufficient conditions are given such that the corresponding Navier-Stokes solutions are shown to satisfy the algebraic bound
Stephen Montgomery-Smith (2005)
Applications of Mathematics
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We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac-like inequalities. As part of our methods, we give a different approach to a priori estimates of Foiaş, Guillopé and Temam.
Philippe Angot, Vít Dolejší, Miloslav Feistauer, Jiří Felcman (1998)
Applications of Mathematics
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We present the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume barycentric mesh, whereas the diffusion term is discretized by piecewise linear nonconforming triangular finite elements. Under the assumption that the triangulations...
Zdeněk Skalák (2002)
Commentationes Mathematicae Universitatis Carolinae
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In the context of suitable weak solutions to the Navier-Stokes equations we present local conditions of Prodi-Serrin’s type on velocity and pressure under which is a regular point of . The conditions are imposed exclusively on the outside of a sufficiently narrow space-time paraboloid with the vertex and the axis parallel with the -axis.