Well-chosen weak solutions of the instationary Navier-Stokes system and their uniqueness

作者：Farwig Reinhard^*; Giga Yoshikazu

来源：Hokkaido Mathematical Journal, 2018, 47(2): 373-385.

DOI：10.14492/hokmj/1529308824

• Navier-Stokes equations
• initial values
• strong L-alpha(s)(L-q)-solutions
• well-chosen weak solutions
• Serrin's uniquenes theorem

We clarify the notion of well-chosen weak solutions of the instationary Navier-Stokes system recently introduced by the authors and P.-Y. Hsu in the article Initial values for the Navier-Stokes equations in spaces with weights in time, Funkcialaj Ekvacioj (2016). Well-chosen weak solutions have initial values in L-sigma(2)(Omega) contained also in a quasi-optimal scaling-invariant space of Besov type such that nevertheless Serrin's Uniqueness Theorem cannot be applied. However, we find universal conditions such that a weak solution given by a concrete approximation method coincides with the strong solution in a weighted function class of Serrin type.

• 出版日期2018-6