This paper deals with the Kato.Ponce - type commutator estimates in the Besov space Bs p, q(ℝn) and the Triebel - Lizorkin space Fs p, q(ℝn) related to the Euler equations describing the motion of perfect incompressible fluids. We investigate the relation between the optimal bound of the commutator estimates and the solvability of the Euler equations. In particular, we show that these commutator estimates fail in Bs p, q(ℝn) and F s p, q(ℝn) with the critical differential order s = n/p + 1 and various exponents p and q.
- Commutator estimates
- Incompressible Euler equations
- The Besov spaces
- The Triebel - Lizorkin spaces
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics