Geodesic
Improved estimates for the sharp interface limit of the stochastic Cahn–Hilliard equation with space-time white noise
Ľubomír Baňas1 ; Jean Daniel Mukam1 orcid
1Bielefeld University, Bielefeld, Germany
Interfaces and free boundaries, Tome 26 (2024) no. 4, pp. 563-586

Voir la notice de l'article provenant de la source EMS Press

DOI

We study the sharp interface limit of the stochastic Cahn–Hilliard equation with cubic double-well potential and additive space-time white noise εσW ̇, where ε>0 is an interfacial width parameter. We prove that, for a sufficiently large scaling constant σ>0, the stochastic Cahn–Hilliard equation converges to the deterministic Mullins–Sekerka/Hele-Shaw problem for ε→0. The convergence is shown in suitable fractional Sobolev norms as well as in the Lp-norm for p∈(2,4] in spatial dimension d=2,3. This generalizes the existing result for the space-time white noise to dimension d=3 and improves the existing results for smooth noise, which were so far limited to p∈(2,d+22d+8​] in spatial dimension d=2,3. As a byproduct of the analysis of the stochastic problem with space-time white noise, we identify minimal regularity requirements on the noise which allow convergence to the sharp interface limit in the H1-norm and also provide improved convergence estimates for the sharp interface limit of the deterministic problem.
DOI : 10.4171/ifb/518
Classification : 35R60, 35K55, 35K91, 35R35, 60H15
Mots-clés : stochastic Cahn–Hilliard equation, space-time white noise, Mullins–Sekerka/Hele-Shaw problem, sharp interface limit

Ľubomír Baňas  1   ; Jean Daniel Mukam  1

1 Bielefeld University, Bielefeld, Germany 
Ľubomír Baňas; Jean Daniel Mukam. Improved estimates for the sharp interface limit of the stochastic Cahn–Hilliard equation with space-time white noise. Interfaces and free boundaries, Tome 26 (2024) no. 4, pp. 563-586. doi: 10.4171/ifb/518
@article{10_4171_ifb_518,
     author = {\v{L}ubom{\'\i}r Ba\v{n}as and Jean Daniel Mukam},
     title = {Improved estimates for the sharp interface limit of the stochastic {Cahn{\textendash}Hilliard} equation with space-time white noise},
     journal = {Interfaces and free boundaries},
     pages = {563--586},
     year = {2024},
     volume = {26},
     number = {4},
     doi = {10.4171/ifb/518},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/518/}
}
TY  - JOUR
AU  - Ľubomír Baňas
AU  - Jean Daniel Mukam
TI  - Improved estimates for the sharp interface limit of the stochastic Cahn–Hilliard equation with space-time white noise
JO  - Interfaces and free boundaries
PY  - 2024
SP  - 563
EP  - 586
VL  - 26
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/518/
DO  - 10.4171/ifb/518
ID  - 10_4171_ifb_518
ER  - 
%0 Journal Article
%A Ľubomír Baňas
%A Jean Daniel Mukam
%T Improved estimates for the sharp interface limit of the stochastic Cahn–Hilliard equation with space-time white noise
%J Interfaces and free boundaries
%D 2024
%P 563-586
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/518/
%R 10.4171/ifb/518
%F 10_4171_ifb_518

Cité par Sources :