Non-negative martingale solutions to the stochastic thin-film equation with nonlinear gradient noise

DOI10.1007/s00205-021-01682-zzbMath1471.35345arXiv2012.04356OpenAlexW3180957612MaRDI QIDQ2049593

Günther Grün, Benjamin Gess, Manuel V. Gnann, Konstantinos Anastasios Dareiotis

Publication date: 27 August 2021

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.04356

zbMATH Keywords

thermal noisenonlinear stochastic scalar conservation law structure

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Initial-boundary value problems for higher-order parabolic equations (35K35) Thin fluid films (76A20) Degenerate parabolic equations (35K65) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (6)

Zero-contact angle solutions to stochastic thin-film equations ⋮ Existence of nonnegative solutions to stochastic thin-film equations in two space dimensions ⋮ The Cox–Voinov law for traveling waves in the partial wetting regime* ⋮ Thermodynamically consistent and positivity-preserving discretization of the thin-film equation with thermal noise ⋮ A note on regularity and separation for the stochastic Allen-Cahn equation with logarithmic potential ⋮ Random separation property for stochastic Allen-Cahn-type equations

Cites Work

• Unnamed Item
• Unnamed Item
• On the regularity for the Navier-slip thin-film equation in the perfect wetting regime
• A relatively short proof of Itô's formula for SPDEs and its applications
• Darcy's flow with prescribed contact angle: well-posedness and lubrication approximation
• Well-posedness for a class of thin-film equations with general mobility in the regime of partial wetting
• Classical solvability of the multidimensional free boundary problem for the thin film equation with quadratic mobility in the case of partial wetting
• Higher order nonlinear degenerate parabolic equations
• Smooth zero-contact-angle solutions to a thin-film equation around the steady state
• Compact sets in the space \(L^ p(0,T;B)\)
• Droplet spreading under weak slippage: The optimal asymptotic propagation rate in the multi-dimensional case.
• Instability, rupture and fluctuations in thin liquid films: theory and computations
• Stability of receding traveling waves for a fourth order degenerate parabolic free boundary problem
• The thin-film equation close to self-similarity
• The Navier-slip thin-film equation for 3D fluid films: existence and uniqueness
• Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation
• Martingale and stationary solutions for stochastic Navier-Stokes equations
• Well-posedness and uniform bounds for a nonlocal third order evolution operator on an infinite wedge
• The thin viscous flow equation in higher space dimensions
• The thin film equation with \(2\leq n < 3\): Finite speed of propagation in terms of the \(L^1\)-norm
• Nonlinear diffusion equations with nonlinear gradient noise
• On temporal regularity of stochastic convolutions in \(2\)-smooth Banach spaces
• The stochastic thin-film equation: existence of nonnegative martingale solutions
• Optimal lower bounds on asymptotic support propagation rates for the thin-film equation
• On uniqueness of weak solutions for the thin-film equation
• Well-posedness for the Navier-slip thin-film equation in the case of complete wetting
• Degenerate parabolic stochastic partial differential equations
• Upper bounds on waiting times for the thin-film equation: the case of weak slippage
• Thin-film flow influenced by thermal noise
• Lower bounds on waiting times for degenerate parabolic equations and systems
• Thin-film equations with ``partial wetting energy: Existence of weak solutions
• A Free Boundary Problem of Fourth Order: Classical Solutions in Weighted Hölder Spaces
• The almost sure Skorokhod representation for subsequences in nonmetric spaces
• Lubrication approximation with prescribed nonzero contact anggle
• On a Fourth-Order Degenerate Parabolic Equation: Global Entropy Estimates, Existence, and Qualitative Behavior of Solutions
• Existence of Positive Solutions to Stochastic Thin-Film Equations
• Droplet Spreading Under Weak Slippage—Existence for the Cauchy Problem
• On the convergence of entropy consistent schemes for lubrication type equations in multiple space dimensions
• Well‐posedness for the Navier Slip Thin‐Film equation in the case of partial wetting
• The Thin Film Equation with Non-Zero Contact Angle: A Singular Perturbation Approach
• Well-Posedness and Self-Similar Asymptotics for a Thin-Film Equation
• Relaxation Rates for a Perturbation of a Stationary Solution to the Thin-Film Equation

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