Abstract
In this paper, we prove that the sequence (un, ϕn) of the Galerkin approximation of the solution (u, ϕ) to a stochastic 2D Cahn-Hilliard-Navier-Stokes model verifies the following convergence result
for any deterministic time T > 0 and for a specified moment function \(\tilde {\psi }(x)\). Also, we provide a result on uniform boundedness of the moment
where ψ grows as a single logarithm at infinity and furthermore, we establih the results on convergence of the Galerkin approximation up to a deterministic time T when the \(\mathbb {V}\)-norm is replaced by the \(\mathbb {H}\)-norm.
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Deugoué, G., Ndongmo Ngana, A. & Tachim Medjo, T. Some convergences results on the stochastic Cahn-Hilliard-Navier-Stokes equations with multiplicative noise. Potential Anal 59, 263–282 (2023). https://doi.org/10.1007/s11118-021-09967-4
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DOI: https://doi.org/10.1007/s11118-021-09967-4