Well-posedness of stochastic partial differential equations with fully local monotone coefficients
type: Item
instance of: scholarly article
title: Well-posedness of stochastic partial differential equations with fully local monotone coefficients
author: Michael Röckner
author: Shijie Shang
author: Tu-Sheng Zhang
published in: Mathematische Annalen
publication date: 2024-10-28T00:00:00Z
review text: The authors establish the wellposedness for stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple which play significant roles in modeling the real world evolution process, such as fluid dynamics, etc. The diffusion coefficient may depend on the gradient of the solution. The authors innovatively combine the pseudo-monotonicity techniques and compactness arguments to obtain the results. This work solves a longstanding open problem and make great progress in this field.
reviewed by: Wenjie Hu
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 49K40
zbMATH DE Number: 7932384
zbMATH Keywords: well-posedness
zbMATH Keywords: stochastic partial differential equations
zbMATH Keywords: local monotone coefficients
zbMATH Keywords: pseudo-monotonicity techniques
zbMATH Keywords: compactness arguments
MaRDI profile type: Publication
cites work: Stopping times and tightness
cites work: Existence and regularity of solution for a stochastic Cahn-Hilliard/Allen-Cahn equation with unbounded noise diffusion
cites work: Stochastic porous media equations
cites work: Q4269108
cites work: Équations et inéquations non linéaires dans les espaces vectoriels en dualité
cites work: Strong solutions for SPDE with locally monotone coefficients driven by Lévy noise
cites work: Stochastic reaction-diffusion equations driven by jump processes
cites work: Some results on the penalised nematic liquid crystals driven by multiplicative noise: weak solution and maximum principle
cites work: Free Energy of a Nonuniform System. I. Interfacial Free Energy
cites work: Q4871637
cites work: Cahn-Hilliard stochastic equation: Existence of the solution and of its density
cites work: Ergodicity of stochastic curve shortening flow in the plane
cites work: Martingale solutions and Markov selections for stochastic partial differential equations
cites work: On stochastic squations with respect to semimartingales III
cites work: Nonlinear evolution equations with nonmonotonic perturbations
cites work: On Weak Solutions of Stochastic Differential Equations II
cites work: Quasilinear parabolic stochastic partial differential equations: existence, uniqueness
cites work: Q3992729
cites work: On the Skorokhod topology
cites work: Variational solutions of stochastic partial differential equations with cylindrical Lévy noise
cites work: Nonparabolic dissipative systems modeling the flow of liquid crystals
cites work: Q5890172
cites work: Existence and uniqueness of solutions to nonlinear evolution equations with locally monotone operators
cites work: Well-posedness of stochastic partial differential equations with Lyapunov condition
cites work: SPDE in Hilbert space with locally monotone coefficients
cites work: Local and global well-posedness of SPDE with generalized coercivity conditions
cites work: Stochastic partial differential equations: an introduction
cites work: A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method
cites work: On the existence and uniqueness of solution to a stochastic 2D Allen–Cahn–Navier–Stokes model
cites work: Monotone (nonlinear) operators in Hilbert space
cites work: Coercivity condition for higher moment a priori estimates for nonlinear SPDEs and existence of a solution under local monotonicity
cites work: Nonlinear stochastic parabolic partial differential equations with a monotone operator of the Ladyzenskaya-Smagorinsky type, driven by a Lévy noise
cites work: Q5646190
cites work: A concise course on stochastic partial differential equations
cites work: Stochastic generalized porous media and fast diffusion equations
cites work: An Introduction to Partial Differential Equations
cites work: Non-monotone stochastic generalized porous media equations
cites work: Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity
cites work: Existence of periodic solutions for nonlinear evolution equations with pseudo monotone operators
cites work: Compact sets in the space \(L^ p(0,T;B)\)
cites work: Navier-Stokes equations. Theory and numerical analysis. Repr. with corr
cites work: Well-posedness for a pseudomonotone evolution problem with multiplicative noise
cites work: Well-posedness for nonlinear SPDEs with strongly continuous perturbation
cites work: Axisymmetric Solutions to Coupled Navier–Stokes/Allen–Cahn Equations
cites work: A diffuse-interface method for simulating two-phase flows of complex fluids
cites work: Q3995594
cites work: ON STOCHASTIC EVOLUTION EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS
DOI: 10.1007/S00208-024-02836-6
description: scientific article; zbMATH DE number 7932384