Removable singularities of weak solutions to the navier-stokes equations |
| |
Authors: | Hideo Kozono |
| |
Institution: | Graduate School of Polymathematics Nagoya University , Nagoya, 464-01, Japan E-mail: kozonoQmath.nagoya-u.ac.jp |
| |
Abstract: | Consider the Navier-Stokes equations in Ω×(0,T), where Ω is a domain in R3. We show that there is an absolute constant ε0 such that ever, y weak solution u with the property that Suptε(a,b)|u(t)|L(D)≤ε0 is necessarily of class C∞ in the space-time variables on any compact suhset of D × (a,b) , where D?? and 0 a<b<T. As an application. we prove that if the weak solution u behaves around (xo, to) εΩ×(o,T) 1ike u(x, t) = o(|x - xo|-1) as x→x 0 uniforlnly in t in some neighbourliood of to, then (xo,to) is actually a removable singularity of u. |
| |
Keywords: | |
|
|