Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	吴政言博士，德国Bielefeld 大学
Inviter:
Title:	Landau-Lifshitz-Navier-Stokes Equations: Large Deviations and Relationship to The Energy Equality
Language:	Chinese
Time & Venue:	2024.02.01 16:00-17:00 南楼613
Abstract:	We study a dynamical large deviation principle for global solutions to the three-dimensional Landau-Lifschitz-Navier-Stokes equations with spatially correlated noise, in a scaling regime where the noise intensity and correlation length go to zero simultaneously. Paralleling the classical Leray theory, the solutions are defined globally in time and satisfy a path-by-path energy inequality. We relate classes of solutions on which the large deviations upper and lower bounds match to the deterministic energy equality, generalising the result of Lions-Ladyzhenskaya, and relate potential failure of the energy equality to violations of the large deviations lower bound without restriction. Finally, we consider the large deviations of the local-in-time strong solution, and show that the solution can rapidly lose regularity with negligible large-deviations cost. This is joint work with Benjamin Gess and Daniel Heydecker.