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- W4362552286 abstract "We consider a 2D stochastic modified Swift-Hohenberg equations with multiplicative noise and periodic boundary. First, we establish the existence of local and global martingale and pathwise solutions in the regular Sobolev space $H^{2m}$ for each $mgeqslant1$. Associated with the unique global pathwise solution, we obtain a Markovian transition semigroup. Then, we show the existence of invariant measures and ergodic invariant measures for this Markovian semigroup on $H^{2m}$. At last, we improve the regularity of the obtained invariant measures to $H^{2(m+1)}$. With appropriate conditions on the diffusion coefficient, we can deduce the infinite regularity of the invariant measures, which was conjectured by Glatt-Holtz textit{et al.} in their situation." @default.
- W4362552286 created "2023-04-06" @default.
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- W4362552286 creator A5056436243 @default.
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- W4362552286 date "2023-04-04" @default.
- W4362552286 modified "2023-09-28" @default.
- W4362552286 title "Global martingale and pathwise solutions and infinite regularity of invariant measures for a stochastic modified Swift–Hohenberg equation" @default.
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- W4362552286 doi "https://doi.org/10.1088/1361-6544/acc6b1" @default.
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