Dynamics Seminar

Event Information Uniform Lyapunov exponents for Hamilton-Jacobi equations at the vanishing viscosity limit
15:10 on Monday April 11, 2022
16:00 on Monday April 11, 2022
BA6183, Bahen Center, 40 St. George St.
Ke Zhang

University of Toronto

It is well known that the viscous Hamilton-Jacobi equation on a compact domain converges exponentially fast to a stationary solution. (For example, Sinai proved this for a random potential on the torus in the late 80s). However, the a priori exponent decreases to 0 as the vicosity decreases to 0. On the other hand, in the zero viscosity case, the solution converges exponentially fast if the associated Lagrangian system admits a unique, hyperbolic minimizing orbit. Does the invicid exponent carry over to systems with small viscosity? We will show that this is the case for a generic "kicked" potential. This is a joint work with Konstantin Khanin and Lei Zhang.