Martingale solutions to the stochastic thin-film equation in two dimensions

被引：1
|
作者：
Sauerbrey, Max [1 ]
机构：
[1] Delft Univ Technol, Delft Inst Appl Math, NL-2628 CD Delft, Netherlands
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2024年 / 60卷 / 01期
关键词：
Thin-film equation; Noise; alpha-Entropy estimates; Stochastic compactness method; EXISTENCE;
D O I：
10.1214/22-AIHP1328
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We construct solutions to the stochastic thin-film equation with quadratic mobility and Stratonovich gradient noise in the physically relevant dimension d = 2 and allow in particular for solutions with non -full support. The construction relies on a Trotter- Kato time -splitting scheme, which was recently employed in d = 1. The additional analytical challenges due to the higher spatial dimension are overcome using alpha-entropy estimates and corresponding tightness arguments.
引用
收藏
页码：373 / 412
页数：40
相关论文
共 50 条
  • [1] The stochastic thin-film equation: Existence of nonnegative martingale solutions
    Gess, Benjamin
    Gnann, Manuel, V
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2020, 130 (12) : 7260 - 7302
  • [2] Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
    Konstantinos Dareiotis
    Benjamin Gess
    Manuel V. Gnann
    Günther Grün
    Archive for Rational Mechanics and Analysis, 2021, 242 : 179 - 234
  • [3] Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
    Dareiotis, Konstantinos
    Gess, Benjamin
    Gnann, Manuel, V
    Gruen, Guenther
    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2021, 242 (01) : 179 - 234
  • [4] Existence of nonnegative solutions to stochastic thin-film equations in two space dimensions
    Metzger, Stefan
    Gruen, Guenther
    INTERFACES AND FREE BOUNDARIES, 2022, 24 (03) : 307 - 387
  • [5] On uniqueness of weak solutions for the thin-film equation
    John, Dominik
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (08) : 4122 - 4171
  • [6] EXISTENCE OF POSITIVE SOLUTIONS TO STOCHASTIC THIN-FILM EQUATIONS
    Fischer, Julian
    Gruen, Guenther
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2018, 50 (01) : 411 - 455
  • [7] Martingale solutions of a stochastic wave equation with reflection
    Kim, Jong Uhn
    JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (09) : 2437 - 2469
  • [8] Soliton solutions of thin-film ferroelectric materials equation
    Sadaf, Maasoomah
    Arshed, Saima
    Akram, Ghazala
    ul Nabi, Andleeb
    Ahmad, Hijaz
    Askar, Sameh
    RESULTS IN PHYSICS, 2024, 58
  • [9] Pressure-dipole solutions of the thin-film equation
    Bowen, M.
    Witelski, T. P.
    EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2019, 30 (02) : 358 - 399
  • [10] Strong solutions and trajectory attractors to the thin-film equation with absorption
    Kapustyan, Oleksiy, V
    Kasyanov, Pavlo O.
    Taranets, Roman M.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 493 (02)
12345