Large deviations for stochastic Kuramoto–Sivashinsky equation with multiplicative noise

• Main Authors: Gregory Amali Paul Rose, Murugan Suvinthra, Krishnan Balachandran
• Format: Article
• Language: English
• Published: Vilnius University Press 2021-07-01
• Series: Nonlinear Analysis
• Subjects: large deviations; stochastic partial differential equations; weak convergence; uniform Laplace principle
• Online Access: https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/24178
• ISSN: 1392-5113; 2335-8963

The Kuramoto–Sivashinsky equation is a nonlinear parabolic partial differential equation, which describes the instability and turbulence of waves in chemical reactions and laminar flames. The aim of this work is to prove the large deviation principle for the stochastic Kuramoto–Sivashinsky equation driven by multiplicative noise. To establish the large deviation principle, the weak convergence approach is used, which relies on proving basic qualitative properties of controlled versions of the original stochastic partial differential equation.