Some convergences results on the stochastic Cahn-Hilliard-Navier-Stokes equations with multiplicative noise
Article
Deugoué, G, Ndongmo Ngana, A, Tachim Medjo, T. (2023). Some convergences results on the stochastic Cahn-Hilliard-Navier-Stokes equations with multiplicative noise
. POTENTIAL ANALYSIS, 59(1), 263-282. 10.1007/s11118-021-09967-4
Deugoué, G, Ndongmo Ngana, A, Tachim Medjo, T. (2023). Some convergences results on the stochastic Cahn-Hilliard-Navier-Stokes equations with multiplicative noise
. POTENTIAL ANALYSIS, 59(1), 263-282. 10.1007/s11118-021-09967-4
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 limn→∞E[supt∈[0,T]ψ~(∥(un(t)),ϕn(t)−(u(t),ϕ(t))∥V2)]=0 for any deterministic time T > 0 and for a specified moment function ψ~ (x). Also, we provide a result on uniform boundedness of the moment Esupt∈[0,T]ψ(∥(u(t),ϕ(t))∥V2) 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 V-norm is replaced by the ℍ-norm.
