The critical variational setting for stochastic evolution equations

• 成果类型: Article
• 署名作者: Agresti, Antonio; Veraar, Mark
• 署名单位: Institute of Science & Technology - Austria; Delft University of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01249-x
• 发表日期: 2024
• 页码: 957-1015
• 关键词: navier-stokes equations; partial-differential-equations; maximal regularity; critical spaces; well-posedness; EXISTENCE; coefficients; uniqueness; driven; spdes

摘要

In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative noise are weakened considerably. Our new setting provides general conditions under which local and global existence and uniqueness hold. In addition, we prove continuous dependence on the initial data. We show that many classical SPDEs, which could not be covered by the classical variational setting, do fit in the critical variational setting. In particular, this is the case for the Cahn-Hilliard equation, tamed Navier-Stokes equations, and Allen-Cahn equation.