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Multiple timescales in the evolution of fluids models

Connections for Women: Dispersive and Stochastic PDE August 19, 2015 - August 21, 2015

August 19, 2015 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Margaret Beck (Boston University)
Location: MSRI: Simons Auditorium
  • 1D Burger's equation

  • Navier-Stokes on torus

  • long range behavior

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



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.

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