Measure attractors for stochastic Navier-Stokes equations.
Capiński, Marek, Cutland, Nigel J. (1998)
Electronic Journal of Probability [electronic only]
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Capiński, Marek, Cutland, Nigel J. (1998)
Electronic Journal of Probability [electronic only]
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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.
Alain Bensoussan, Jens Frehse (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Manfred Müller, Joachim Naumann (1978)
Aplikace matematiky
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The paper present an existence theorem for a strong solution to an abstract evolution inequality where the properties of the operators involved are motivated by a type of modified Navier-Stokes equations under certain unilateral boundary conditions. The method of proof rests upon a Galerkin type argument combined with the regularization of the functional.
Alain Bensoussan, Jens Frehse (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this article we consider local solutions for stochastic Navier Stokes equations, based on the approach of Von Wahl, for the deterministic case. We present several approaches of the concept, depending on the smoothness available. When smoothness is available, we can in someway reduce the stochastic equation to a deterministic one with a random parameter. In the general case, we mimic the concept of local solution for stochastic differential equations.