Using the Maxwell-Higgs model, we prove that linearly unstable symmetric vortices in the Ginzburg-Landau theory are dynamically unstable in the H1 norm (which is the natural norm for the problem). In this work we study the dynamic instability of the radial solutions of the Ginzburg-Landau equations in R2 (...)
This short note is to announce our recent results [2,3] which provide a complete mathematical proof of the viscous destabilization phenomenon, pointed out by Heisenberg (1924), C.C. Lin and Tollmien (1940s), among other prominent physicists. Precisely, we construct growing modes of the linearized Navier-Stokes equations about general stationary shear flows in a bounded channel (channel flows) or on a half-space (boundary layers), for sufficiently large Reynolds number . Such an instability is linked...
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