Existence and uniqueness of weak solution to a three-dimensional stochastic modified-Leray-alpha model of fluid turbulence

Selmi, Ridha; Nasfi, Rim

doi:10.15559/21-vmsta175

Cited by 3 publications

(1 citation statement)

References 19 publications

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“…For the real problems in engineering, fundamental theories on the uniqueness and existence of solutions is very important, and cannot be ignored. Many results have been obtained in the literature regarding this; see [11][12][13][14][15][16][17]. Ref.…”

Section: Introductionmentioning

confidence: 98%

Fundamental Properties of Nonlinear Stochastic Differential Equations

Liu

Deng

et al. 2022

Mathematics

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The existence of solutions is used the premise of discussing other properties of dynamic systems. The goal of this paper is to investigate the fundamental properties of nonlinear stochastic differential equations via the Khasminskii test, including the local existence and global existence of the solutions. Firstly, a fundamental result is given as a lemma to verify the local existence of solutions to the considered equation. Then, the equivalent proposition for the global existence and the fundamental principle for the Khasminskii test are formally established. Moreover, the classical Khasminskii test is generalized to the cases with high-order estimates and heavy nonlinearity for the stochastic derivatives of the Lyapunov functions. The role of the noise in this aspect is especially investigated, some concrete criteria are obtained, and an application for the role of the noise in the persistence of financial systems is accordingly provided. As another application of the fundamental principle, a new version of the Khasminskii test is established for the delayed stochastic systems. Finally the conclusions obtained in the paper are verified by simulation. The results show that, under weaker conditions, the global existence of better solutions to stochastic systems to those in the existing literature can be obtained.

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Section: Introductionmentioning

confidence: 98%

Fundamental Properties of Nonlinear Stochastic Differential Equations

Liu

Deng

et al. 2022

Mathematics

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Well-posedness and convergence results for the 3D-Lagrange Boussinesq-$$\alpha $$ system

Sboui

Selmi

2022

Arch. Math.

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Global in time well-posedness of a three-dimensional periodic regularized Boussinesq system

Almutairi

2024

Demonstratio Mathematica

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Global in time weak solution to a regularized periodic three-dimensional Boussinesq system is proved to exist in energy spaces. This solution depends continuously on the initial data. In particular, it is unique. The main novelty is the global in time aspect of this solution. The proofs use the coupling between the temperature and the velocity of the fluid, energy methods, and compactness argument.

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Existence and uniqueness of weak solution to a three-dimensional stochastic modified-Leray-alpha model of fluid turbulence

Abstract: In this paper, we study the stochastic three-dimensional modified Leray-alpha model arising from the turbulent flows of fluids. We prove the existence of the probabilistic weak solution under the non-Lipschitz condition for the nonlinear forcing terms. We also discuss its uniqueness.

Cited by 3 publications

References 19 publications

Fundamental Properties of Nonlinear Stochastic Differential Equations

Fundamental Properties of Nonlinear Stochastic Differential Equations

Well-posedness and convergence results for the 3D-Lagrange Boussinesq-$$\alpha $$ system

Global in time well-posedness of a three-dimensional periodic regularized Boussinesq system

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