Uniqueness theorems for the three dimensional Navier-Stokes system
The author considers the following class of systems of Navier-Stokes type: \[ v_t-\nu\Delta v=Q(v,v) \text{ in }\mathbb{R}^d \times(0,T),\qquad v(0) =v_0\quad \text{ in }\mathbb{R}^d \] for \(d\geq 3\). The operator \(Q\) has the form \[ Q(v,v)= \sum_{j,k}A_{j,k} (D)(v^jv^k), \] where the \(A_{j,k}\) are Fourier multiplication operators that are homogeneous of degree 1. The main results of the paper are existence and uniqueness theorems for functions with values in Besov spaces.
scientific article; zbMATH DE number 1309899
scientific article