Existence and Exponential Behavior for the Stochastic 2D Cahn–Hilliard–Oldroyd Model of Order One

Deugoué, G.; Moghomye, B. Jidjou; Medjo, T. Tachim

doi:10.1007/s00021-021-00647-2

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…We can easily check that (see [11]) the maps B, R and E are locally Lipschitz continuous i.e. for every r > 0, there exists a constant C r such that…”

mentioning

confidence: 99%

Wong-zakai Approximation for a Stochastic 2D Cahn-hilliard-navier-stokes Model

Medjo

2023

Preprint

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In this paper, we demonstrate the Wong-Zakai approximation results for two dimensional stochastic Cahn-Hilliard-Navier-Stokes model. The model consists of a Navier-Stokes system coupled with a convective Cahn-Hilliard equations. It describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids under the influence of multiplicative noise. Our main result describes the support of the distribution of solutions. As in [2], both inclusions are proved by means of a general Wong-Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert-valued Brownian motion and some adapted finite dimensional approximation of this process. Note that the coupling between the Navier-Stokes system and the Cahn-Hilliard equations makes the analysis more involved.

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“…We can easily check that (see [11]) the maps B, R and E are locally Lipschitz continuous i.e. for every r > 0, there exists a constant C r such that…”

mentioning

confidence: 99%

Wong-zakai Approximation for a Stochastic 2D Cahn-hilliard-navier-stokes Model

Medjo

2023

Preprint

View full text Add to dashboard Cite

show abstract

Wong–Zakai approximation for a stochastic 2D Cahn–Hilliard–Navier–Stokes model

Medjo

2024

Mathematische Nachrichten

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In this paper, we demonstrate the Wong–Zakai approximation results for two dimensional stochastic Cahn–Hilliard–Navier–Stokes model. The model consists of a Navier–Stokes system coupled with convective Cahn–Hilliard equations. It describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids under the influence of multiplicative noise. Our main result describes the support of the distribution of solutions. As in [2], both inclusions are proved by means of a general Wong–Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert‐valued Brownian motion and some adapted finite‐dimensional approximation of this process. Note that the coupling between the Navier–Stokes system and the Cahn–Hilliard equations makes the analysis more involved.

show abstract