Comments on Navier-Stokes equations with Navier boundary conditions for a bounded domain in the plane. SIAM Journal on Mathematical Analysis, Vol 38(1) 2006 p. 210-232:
- I say that Equation (2.5) p. 214 follows from the standard trace theorem, Sobolev interpolation, and Poincare's inequality. In fact, the first inequality is an elementary trace theorem (for a proof, see the first comment on Chapter 3 in "Things I should or shouldn't have said in my thesis"). The second inequality follows from the first using Poincare's inequality, or follows directly using a standard trace theorem and Poincare's inequality. In any case, Sobolev interpolation never enters in.
- There is a small typo on p. 220: containment (subset sign) should be contains (superset sign) in the relation between L^\iny and H^{1/2 + \eps} + C^{1/2 + \eps}.
