Nonuniqueness in fluid models through bifurcations
It is well known in physics literature, despite almost no mathematical results, that the steady states of fluid model equations are not unique and appear through bifurcations when the Reynolds number increases. After presenting this, the same methodology will be used for time-dependent problems to obtain the non-uniqueness of solutions to Cauchy problems. Numerical non-uniqueness results will be presented for the Navier-Stokes equations in both two and three dimensions as well as for the complex Ginzburg-Landau equation. The physical implications will be discussed in particular. Joint works with Dallas Albritton, Mikhail Korobkov, Xiao Ren, and Vladimír Šverák.