Events for 01/26/2021 from all calendars

Nonlinear Partial Differential Equations

Time: 3:00PM - 00:00AM

Location: Zoom

Speaker: Luan Hoang, Texas Tech University

Title: The Navier-Stokes equations: asymptotic expansions for solutions and their associated Lagrangian trajectories

Abstract: We study the long-time dynamics of viscous incompressible fluids for both Eulerian and Lagrangian descriptions. For the Eulerian description, a solution of the Navier-Stokes equations with a potential admits a Foias-Saut asymptotic expansion as time tends to infinity. This expansion provides very precise asymptotic approximations of the solution in terms of polynomial and exponential functions. The result is extended to many related Navier-Stokes systems including the Navier-Stokes equations of rotating fluids and the Navier-Stokes-Boussinesq system. For the Lagrangian description, we prove that the trajectories of the fluid particles also have similar asymptotic expansions. This is established by studying the system of nonlinear ordinary differential equations relating the Lagrangian trajectories to the solutions of the Navier-Stokes equations.