Abstract
We investigate very weak solutions to the instationary Navier–Stokes system being contained in \({L^r(0,T; L^q(\Omega))}\) where \({\Omega\subseteq\mathbb {R}^n}\) is a bounded domain and \({\frac{2}{r}+\frac{n}{q}\leq 1}\) . The chosen space of data is small enough to guarantee uniqueness of solutions and existence in case of small data or short time intervals. On the other hand, the data space is large enough that every vector field in \({L^r(0,T;L^q_\sigma(\Omega))}\) is a very weak solution for appropriate data. The solutions and the data depend continuously on each other.
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Riechwald, P.F., Schumacher, K. A large class of solutions for the instationary Navier–Stokes system. J. Evol. Equ. 9, 593–611 (2009). https://doi.org/10.1007/s00028-009-0025-7
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DOI: https://doi.org/10.1007/s00028-009-0025-7