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• W4313462774 abstract "Abstract We consider in dimensions <?CDATA $d = 1,2,3$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:math> the ɛ -dependent stochastic Cahn–Hilliard equation with a multiplicative and sufficiently regular in space infinite dimensional Fourier noise with strength of order <?CDATA $mathcal{O}(varepsilon^gamma)$?> , γ > 0. The initial condition is non-layered and independent from ɛ . Under general assumptions on the noise diffusion σ , we prove moment estimates in H 1 (and in <?CDATA $L^infty$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msup> <mml:mi>L</mml:mi> <mml:mi mathvariant=normal>∞</mml:mi> </mml:msup> </mml:math> when d = 1). Higher H 2 regularity p -moment estimates are derived when σ is bounded, yielding as well space Hölder and <?CDATA $L^infty$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msup> <mml:mi>L</mml:mi> <mml:mi mathvariant=normal>∞</mml:mi> </mml:msup> </mml:math> bounds for <?CDATA $d = 2,3$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:math> , and path a.s. continuity in space. All appearing constants are expressed in terms of the small positive parameter ɛ . As in the deterministic case, in H 1 , H 2 , the bounds admit a negative polynomial order in ɛ . Finally, assuming layered initial data of initial energy uniformly bounded in ɛ , as proposed by Chen (1996 J. Differ. Geom. 44 262–311), we use our H 1 2d-moment estimate and prove the stochastic solution’s convergence to <?CDATA ${pm}1$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mrow> <mml:mo>±</mml:mo> </mml:mrow> <mml:mn>1</mml:mn> </mml:math> as <?CDATA $varepsilonrightarrow 0$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi>ε</mml:mi> <mml:mo stretchy=false>→</mml:mo> <mml:mn>0</mml:mn> </mml:math> a.s. when the noise diffusion has a linear growth." @default.
• W4313462774 created "2023-01-06" @default.
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• W4313462774 date "2023-01-03" @default.
• W4313462774 modified "2023-10-14" @default.
• W4313462774 title "Higher moments for the stochastic Cahn–Hilliard equation with multiplicative Fourier noise" @default.
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• W4313462774 doi "https://doi.org/10.1088/1361-6544/acadc9" @default.
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