Bursting Dynamics of the 3D Euler Equations in Cylindrical Domains

François Golse (1, 2) , Alex Mahalov (3) , Basil Nicolaenko (3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LJLL - Laboratoire Jacques-Louis Lions
3 Department of Mathematics and Statistics [Tempe, Arizona]

A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically resonant cylinders. Resonances of fast swirling Beltrami waves deplete the Euler nonlinearity. The resonant Euler equations are systems of three-dimensional rigid body equations, coupled or not. Some cases of these resonant systems have homoclinic cycles, and orbits in the vicinity of these homoclinic cycles lead to bursts of the Euler solution measured in Sobolev norms of order higher than that corresponding to the enstrophy.

Mots clés: Incompressible Euler Equations; Rotating Fluids; Rigid Body Dynamics; Enstrophy Bursts

Domaines: Equations aux dérivées partielles [math.AP]

François Golse, Alex Mahalov, Basil Nicolaenko. Bursting Dynamics of the 3D Euler Equations in Cylindrical Domains. C. Bardos, A. Fursikov. Instability in Models Connected with Fluid Flows I, Springer Verlag, pp.301-338, 2008, International Mathematical Series, vol. 6. ⟨hal-00139624⟩