Smooth solutions for the dyadic model

Abstract

We consider the dyadic model, which is a toy model to test issues of well-posedness and blow-up for the Navier-Stokes and Euler equations. We prove well-posedness of positive solutions of the viscous problem in the relevant scaling range which corresponds to Navier-Stokes. Likewise we prove well-posedness for the inviscid problem (in a suitable regularity class) when the parameter corresponds to the strongest transport effect of the non-linearity.

References in corpus (2)

• An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture
• The vanishing viscosity limit for a dyadic model

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