On characteristic exponents in turbulence (Q1080313)

Ruelle has found upper bounds to the magnitude and to the number of non- negative characteristic exponents for the Navier-Stokes flow of an impompressible fluid in a domain \(\Omega\). The latter is particularly important because it yields an upper bound to the Hausdorff dimension of attracting sets. However, Ruelle's bound on the number has three deficiencies: (i) it relies on some unproved conjectures about certain constants: (ii) it is valid only in dimensions \(\geq 3\) and not 2; (iii) it is valid only in the limit \(\Omega\) \(\to \infty\). In this paper these deficiences are remedied and, in addition, the final constants in the inequality are improved.