Short Communication:The Almost Sure Skorokhod Representation for Subsequences in Nonmetric Spaces

Jakubowski, Adam

doi:10.1137/s0040585x97976052

Cited by 140 publications

(128 citation statements)

References 8 publications

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“…The path space X is not a Polish space and so our compactness argument is based on the Jakubowski-Skorokhod representation theorem instead of the classical Skorokhod representation theorem, see [15]. To be more precise, passing to a weakly convergent subsequence µ ε (and denoting by µ the limit law) we infer the following result.…”

Section: Discussionmentioning

confidence: 99%

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Incompressible Limit for Compressible Fluids with Stochastic Forcing

Breit¹,

Feireisl

Hofmanová

2016

Arch Rational Mech Anal

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Abstract. We study the asymptotic behavior of the isentropic Navier-Stokes system driven by a multiplicative stochastic forcing in the compressible regime, where the Mach number approaches zero. Our approach is based on the recently developed concept of weak martingale solution to the primitive system, uniform bounds derived from a stochastic analogue of the modulated energy inequality, and careful analysis of acoustic waves. A stochastic incompressible Navier-Stokes system is identified as the limit problem.

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Section: Discussionmentioning

confidence: 99%

“…Let us recall their definition introduced in [15]. Among the properties of quasi-Polish spaces used in the main body of this paper belongs the following Jakubowski-Skorokhod representation theorem, see [15,Theorem 2].…”

Section: Proof Of Theorem 211mentioning

confidence: 99%

Incompressible Limit for Compressible Fluids with Stochastic Forcing

Breit¹,

Feireisl

Hofmanová

2016

Arch Rational Mech Anal

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“…In addition, in view of the representation theorem of Jakubowski [13] and the way the weak solutions are being constructed in [2], we may assume, without lost of generality, that stochastic basis Ω, F, {F t } t≥0 , P as well as the Wiener process W coincide for all ε > 0.…”

Section: Solutions Of the Navier-stokes Systemmentioning

confidence: 99%

Compressible Fluids Driven by Stochastic Forcing: The Relative Energy Inequality and Applications

Breit

Feireisl

Hofmanová³

2017

Commun. Math. Phys.

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We show the relative energy inequality for the compressible Navier-Stokes system driven by a stochastic forcing. As a corollary, we prove the weak-strong uniqueness property (pathwise and in law) and convergence of weak solutions in the inviscid-incompressible limit. In particular, we establish a Yamada-Watanabe type result in the context of the compressible Navier-Stokes system, that is, pathwise weak-strong uniqueness implies weak-strong uniqueness in law.

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“…This situation is not covered by the classical Skorokhod Theorem. However, a generalization of it -the JakubowskiSkorokhod Theorem, see [28] -applies to quasi-polish spaces (also used in [8]). This includes weak topologies of Banach spaces.…”

Section: Non-stationary Flowsmentioning

confidence: 99%

Existence Theory for Stochastic Power Law Fluids

Breit

2015

J. Math. Fluid Mech.

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abstract:We consider the equations of motion for an incompressible Non-Newtonian fluid in a bounded Lipschitz domain G ⊂ R d during the time interval (0, T ) together with a stochastic perturbation driven by a Brownian motion W. The balance of momentum reads aswhere v is the velocity, π the pressure and f an external volume force. We assume the common power law model S(ε(v)) = 1 + |ε(v)| p−2 ε(v) and show the existence of weak (martingale) solutions pro-Our approach is based on the L ∞ -truncation and a harmonic pressure decomposition which are adapted to the stochastic setting.

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Short Communication:The Almost Sure Skorokhod Representation for Subsequences in Nonmetric Spaces

Abstract: It is shown that in a large class of topological spaces every uniformly tight sequence of random elements contains a subsequence which admits the usual almost sure (a.s.) Skorokhod representation on the Lebesgue interval.

Cited by 140 publications

References 8 publications

Incompressible Limit for Compressible Fluids with Stochastic Forcing

Incompressible Limit for Compressible Fluids with Stochastic Forcing

Compressible Fluids Driven by Stochastic Forcing: The Relative Energy Inequality and Applications

Existence Theory for Stochastic Power Law Fluids

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