The critical variational setting for stochastic evolution equations

DOI10.1007/s00440-023-01249-xarXiv2206.00230OpenAlexW4391473755MaRDI QIDQ6193768

Mark C. Veraar, Antonio Agresti

Publication date: 19 March 2024

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.00230

zbMATH Keywords

coercivitystochastic partial differential equationsvariational methodsCahn-Hilliard equationSwift-Hohenberg equationgeneralized Burgers equationAllen-Cahn equationstochastic evolution equationscritical nonlinearitiestamed Navier-Stokesquasi- and semi-linear

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Monotone operators and generalizations (47H05) Abstract parabolic equations (35K90) Navier-Stokes equations (35Q30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Nonlinear evolution equations (47J35) Quasilinear parabolic equations (35K59)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tightness for a stochastic Allen-Cahn equation
• Stochastic partial differential equations: an introduction
• SPDE in Hilbert space with locally monotone coefficients
• Addendum to the paper ``On quasilinear parabolic evolution equations in weighted \(L_p\)-spaces II
• On quasilinear parabolic evolution equations in weighted \(L_p\)-spaces. II
• Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity
• Strong pathwise solutions of the stochastic Navier-Stokes system
• A variational approach to dissipative SPDEs with singular drift
• Critical spaces for quasilinear parabolic evolution equations and applications
• Strong solutions for stochastic partial differential equations of gradient type
• \(L_p\)-estimates for SPDE with discontinuous coefficients in domains
• On strongly Petrovskiĭ's parabolic SPDEs in arbitrary dimension and application to the stochastic Cahn-Hilliard equation
• Nonlinear parabolic stochastic evolution equations in critical spaces. II: Blow-up criteria and instantaneous regularization
• Stochastic tamed Navier-Stokes equations on \(\mathbb{R}^3\): the existence and the uniqueness of solutions and the existence of an invariant measure
• Stochastic maximal regularity for rough time-dependent problems
• Variational solutions to nonlinear stochastic differential equations in Hilbert spaces
• On stochastic partial differential equations with variable coefficients in \(C^1\) domains
• Strong solutions for SPDE with locally monotone coefficients driven by Lévy noise
• Equations aux dérivées partielles stochastiques non linéaires. I
• Analysis in Banach Spaces
• On stochastic squations with respect to semimartingales III
• Stochastic Navier--Stokes Equations for Turbulent Flows
• Stochastic Cahn-Hilliard equation
• Coercivity condition for higher moment a priori estimates for nonlinear SPDEs and existence of a solution under local monotonicity
• Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence*
• A variational approach to nonlinear stochastic differential equations with linear multiplicative noise
• Doubly nonlinear stochastic evolution equations
• A Stochastic Gronwall Lemma and Well-Posedness of Path-Dependent SDEs Driven by Martingale Noise
• Foundations of Modern Probability
• Stochastic Equations in Infinite Dimensions
• INTERPOLATION OF HILBERT AND SOBOLEV SPACES: QUANTITATIVE ESTIMATES AND COUNTEREXAMPLES
• The stochastic Swift–Hohenberg equation
• Small-Scale Structure of a Scalar Field Convected by Turbulence
• Interpolation in $L^{p}$ with boundary conditions
• Reaction-diffusion equations with transport noise and critical superlinear diffusion: local well-posedness and positivity
• Doubly nonlinear stochastic evolution equations. II.

This page was built for publication: The critical variational setting for stochastic evolution equations