The trend to equilibrium is ascertained for potential motion solutions of a class of systems of nonlinear PDE –the inviscid Burgers equations on tori of any dimension– in the framework of the weak KAM theory. For large time these solutions tend to stationary solutions at a well precise energy (Man ̃ ́e) critical level, which is independent of initial data. An analogous behaviour is foreseen for the Madelung fluid in the semi-classical limit → 0.
Fluid Dynamical Features of the Weak KAM Theory
CARDIN, FRANCO
2008
Abstract
The trend to equilibrium is ascertained for potential motion solutions of a class of systems of nonlinear PDE –the inviscid Burgers equations on tori of any dimension– in the framework of the weak KAM theory. For large time these solutions tend to stationary solutions at a well precise energy (Man ̃ ́e) critical level, which is independent of initial data. An analogous behaviour is foreseen for the Madelung fluid in the semi-classical limit → 0.
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