A Condition Implying Regularity of the Three Dimensional Navier-stokes Equation
نویسنده
چکیده
Abstract. This paper presents a logarithmic improvement to the usual Prodi-Serrin conditions. After this paper was written and widely dispersed, the author realised that there is a much simpler and more standard proof of the main result. This paper (which is now a draft) first presents the simpler proof, and then presents the original more complicated proof. It is shown that if u is the solution to the three dimensional Navier-Stokes equation, then a sufficient condition for regularity is that ∫ T 0 ‖u(t)‖pq/(1 + log ‖u(t)‖q) dt < ∞, for all T > 0, and some 2 < p < ∞, 3 < q < ∞, 2 p + 3 q = 1. This represents a logarithmic improvement over the usual Prodi-Serrin conditions.
منابع مشابه
Conditions Implying Regularity of the Three Dimensional Navier-stokes Equation
We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like inequalities. As part of the our methods, we give a different approach to a priori estimates of Foiaş, Guillopé and Temam.
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