On the Yudovich's type solutions for the 2D Boussinesq system with thermal diffusivity

Paicu, Marius; Zhu, Ning

doi:10.3934/dcds.2020242

Cited by 9 publications

(5 citation statements)

References 34 publications

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“…In [13], Danchin and Paicu proved global well posedness of (1.2) for Yudovich-type initial data, i.e. ω 0 ∈ L ∞ (T 2 ) and the initial temperature θ 0 fulfils a natural additional condition; see [31] for related recent results.…”

Section: Deterministic 2d Boussinesq Systemmentioning

confidence: 99%

Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system

Luo

2021

Nonlinearity

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The inviscid 2D Boussinesq system with thermal diffusivity and multiplicative noise of transport type is studied in the L 2-setting. It is shown that, under a suitable scaling of the noise, weak solutions to the stochastic 2D Boussinesq equations converge weakly to the unique solution of the deterministic viscous Boussinesq system. Consequently, the transport noise asymptotically regularises the inviscid 2D Boussinesq system and enhances dissipation in the limit.

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Section: Deterministic 2d Boussinesq Systemmentioning

confidence: 99%

Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system

Luo

2021

Nonlinearity

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“…Similarly to the theory of 2D Euler equations, it is easy to show that (1.2) admits a weak solution for any L 2 -initial data (θ 0 , ω 0 ), but the uniqueness is open. In [13], Danchin and Paicu proved global well posedness of (1.2) for Yudovich-type initial data, i.e., ω 0 ∈ L ∞ (T 2 ) and the initial temperature θ 0 fulfils a natural additional condition; see [31] for related recent results.…”

Section: Deterministic 2d Boussinesq Systemmentioning

confidence: 99%

Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system

Luo

2020

Preprint

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The inviscid 2D Boussinesq system with thermal diffusivity and multiplicative noise of transport type is studied in the L 2 -setting. It is shown that, under a suitable scaling of the noise, weak solutions to the stochastic 2D Boussinesq equations converge weakly to the unique solution of the deterministic viscous Boussinesq system. Consequently, the transport noise asymptotically regularizes the inviscid 2D Boussinesq system and enhances dissipation in the limit.

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“…In the same way, Hassainia and Hmidi in [26] stated recently an even more accurate result on the local well-posedness problem for (EB) in the context of a regular/singular patch. For more related subject we refer to [19,20,33,36,37,45].…”

Section: (Eb)mentioning

confidence: 99%

Local persistence of geometric structures of the inviscid nonlinear Boussinesq system

Melkemi,

Zerguine

2020

Preprint

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Inspired by the recently published paper [26], the current paper investigates the local well-posedness for the generalized 2d−Boussinesq system in the setting of regular/singular vortex patch. Under the condition that the initial vorticity ω 0 = 1 D 0 , with ∂ D 0 is a Jordan curve with a Hölder regularity C 1+ε , 0 < ε < 1 and the density is a smooth function, we show that the velocity vector field is locally well-posed and we also establish local-in-time regularity persistence of the advected patch. Although, in the case of the singular patch, the analysis is rather complicated due to the coupling phenomena of the system and the structure of the patch. For this purpose, we must assume that the initial nonlinear term is constant around the singular part of the patch boundary.

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On the Yudovich's type solutions for the 2D Boussinesq system with thermal diffusivity

Cited by 9 publications

References 34 publications

Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system

Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system

Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system

Local persistence of geometric structures of the inviscid nonlinear Boussinesq system

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