<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e57" altimg="si3.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math>-solutions for stochastic Navier–Stokes equations with jump noise

Zhu, Jiahui; Brzeźniak, Zdzisław; Liu, Wei

doi:10.1016/j.spl.2019.108563

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Statistics & Probability Letters

2019

DOI: 10.1016/j.spl.2019.108563

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Lp-solutions for stochastic Navier–Stokes equations with jump noise

Jiahui Zhu

Zdzisław Brzeźniak

Wei Liu

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Cited by 8 publications

(1 citation statement)

References 21 publications

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“…for all t ∈ [0, T ]. The existence of pathwise mild solutions for 2D and 3D NSE perturbed by Gaussian as well as jump noise is available in [8,13,22,33], etc and the references therein.…”

mentioning

confidence: 99%

Moderate deviation principle for the 2D stochastic convective Brinkman–Forchheimer equations

Mohan

2020

Stochastics

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This work addresses some asymptotic behavior of solutions to the stochastic convective Brinkman-Forchheimer (SCBF) equations perturbed by multiplicative Gaussian noise in bounded domains. Using a weak convergence approach of Budhiraja and Dupuis, we establish the Laplace principle for the strong solution to the SCBF equations in a suitable Polish space. Then, the Wentzell-Freidlin large deviation principle is derived using the well known results of Varadhan and Bryc. The large deviations for short time are also considered in this work. Furthermore, we study the exponential estimates on certain exit times associated with the solution trajectory of the SCBF equations. Using contraction principle, we study these exponential estimates of exit times from the frame of reference of Freidlin-Wentzell type large deviations principle. This work also improves several LDP results available in the literature for the tamed Navier-Stokes equations as well as Navier-Stokes equations with damping in bounded domains.

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“…for all t ∈ [0, T ]. The existence of pathwise mild solutions for 2D and 3D NSE perturbed by Gaussian as well as jump noise is available in [8,13,22,33], etc and the references therein.…”

mentioning

confidence: 99%

Moderate deviation principle for the 2D stochastic convective Brinkman–Forchheimer equations

Mohan

2020

Stochastics

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Stochastic Fubini Theorem for Jump Noises in Banach Spaces

Zhu

Liu

2020

Acta. Math. Sin.-English Ser.

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$${\mathbb {L}}^p$$-solutions of deterministic and stochastic convective Brinkman–Forchheimer equations

Mohan

2021

Anal.Math.Phys.

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Lp-solutions for stochastic Navier–Stokes equations with jump noise

Cited by 8 publications

References 21 publications

Moderate deviation principle for the 2D stochastic convective Brinkman–Forchheimer equations

Moderate deviation principle for the 2D stochastic convective Brinkman–Forchheimer equations

Stochastic Fubini Theorem for Jump Noises in Banach Spaces

$${\mathbb {L}}^p$$-solutions of deterministic and stochastic convective Brinkman–Forchheimer equations

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