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 every weak solution u with the property that supt∈(a,b) ∥u(t)∥L3W(D) ≤ ε0 is necessarily of class C∞ in the space-time variables on any compact subset of D x (a, b), where D ⊂⊂ Ω and 0 < a < b < T. As an application, we prove that if the weak solution u behaves around (x0, t0) ∈ Ω × (0,T) like u(x,t) = 0(|x - x0l-1) as x → x0 uniformly in t in some neighbourhood of t0, then (x0,t0) is actually a removable singularity of u.
|Number of pages||18|
|Journal||Communications in Partial Differential Equations|
|Publication status||Published - 1998 Jan 1|
ASJC Scopus subject areas
- Applied Mathematics