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

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]).