Numerical Analysis Seminars: Sharp constants for the L∞-norm on the torus and applications to dissipative partial differential equations
14 March 2014 14:00 in CM105
In this seminar we will obtain sharp estimates for the constants appearing in the Sobolev
embedding theorem for the L∞ norm on the d−dimensional torus for d=1,2,3.
The sharp constants are expressed in terms of the Riemann zeta-function,
the Dirichlet beta-series and various lattice sums. We then illustrate our results by
analyzing the solutions of the Swift-Hohenberg equation and (time permitting)
the two dimensional Navier-Stokes equations.
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