CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

April 20, 2021 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

Non-uniqueness and error bounds for fluid flow

Seminar presented by Alberto Bressan (Penn State University, USA)

For hyperbolic systems of conservation laws in one space dimension, a general existence-uniqueness theory is now available, for entropy weak solutions with bounded variation. In several space dimensions, however, it seems unlikely that a similar theory can be achieved.

For the 2-D Euler equations, in this talk I shall discuss the simplest possible examples of Cauchy problems admitting multiple solutions. Several numerical simulations will be presented, for incompressible as well as compressible flow, indicating the existence of two distinct solutions for the same initial data. Typically, one of the solutions contains a single spiraling vortex, while the other solution contains two vortices.

Some theoretical work, aimed at validating the numerical results, will also be discussed.