Multiple timescales in the evolution of fluids models
Connections for Women: Dispersive and Stochastic PDE August 19, 2015 - August 21, 2015
Location: SLMath: Eisenbud Auditorium
1D Burger's equation
Navier-Stokes on torus
long range behavior
55U40 - Topological categories, foundations of homotopy theory
65F05 - Direct numerical methods for linear systems and matrix inversion
14324
The evolution of fluids is known (eg via experiments and numerical studies) to occur on multiple timescales. We discuss how this can be analyzed rigorously in two fundamental models of fluids: the 1D Burgers equation and the 2D Navier-Stokes equation. For Burgers equation, we provide a complete geometric explanation involving invariant manifolds in the phase space of the evolution. For Navier-Stokes on the 2D torus, we discuss two complementary approaches. The first involves the theory of hypocoercive operators, and the second involves invariant manifolds and geometric singular perturbation theory in the Fourier phase space.
14324
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