Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains
The non-stationary Navier-Stokes system in a unbounded \(C^2\)-domain \(\Omega\subset \mathbb{R}^n\), \(n\geq 3\) is considered. After presenting the space \(\tilde{L}^q (\Omega)\), the definition of ``mild solution'' for the Navier-Stokes system with initial velocity \(\mathbf{u}_0\) is given. The main result is represented by the existence of mild solutions. A local uniqueness result is also obtained. A discussion concerning the relation between mild solutions and very weak solutions is provided.
scientific article; zbMATH DE number 6494620
scientific article