Weak and Strong Solutions to Nonlinear SPDEs with Unbounded Noise

2024/01/18 by Goodair, Daniel · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2401.10076

Abstract

We introduce an extended variational framework for nonlinear SPDEs with unbounded noise, defining three different solution types of increasing strength along with criteria to establish their existence. The three notions can be understood as probabilistically and analytically weak, probabilistically strong and analytically weak, as well as probabilistically and analytically strong. Our framework facilitates several well-posedness results for the Navier-Stokes Equation with transport noise, equipped with the no-slip and Navier boundary conditions.

Cited by

• Itô-Stratonovich Conversion in Infinite Dimensions for Unbounded, Time-Dependent, Nonlinear Operators

Related

• Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations
• Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs
• The Zero Viscosity Limit of Stochastic Navier-Stokes Flows
• Existence and Uniqueness of Maximal Solutions to SPDEs with Applications to Viscous Fluid Equations
• Navier-Stokes Equations with Navier Boundary Conditions and Stochastic Lie Transport: Well-Posedness and Inviscid Limit