New results on the constants in some inequalities for the Navier–Stokes quadratic nonlinearity

摘要

We give fully explicit upper and lower bounds for the constants in two known inequalities related to the quadratic nonlinearity of the incompressible (Euler or) Navier–Stokes equations on the torus Td. These inequalities are “tame” generalizations (in the sense of Nash–Moser) of the ones analyzed in the previous works (Morosi and Pizzocchero (2013) [6]).