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
Smooth solutions for the dyadic model
ROMITO, MARCO
2011-01-01
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-linearityFile in questo prodotto:
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