Abstract
We investigate several aspects of very weak solutions u to stationary and nonstationary Navier-Stokes equations in a bounded domain Ω \( \subseteq \) ℝ3. This notion was introduced by Amann [3], [4] for the nonstationary case with nonhomogeneous boundary data u|ϕΩ = g leading to a new and very large solution class. Here we are mainly interested to investigate the ‘largest possible’ class for the more general problem with arbitrary divergence k = div u, boundary data g = u|ϕΩ. and an external force f, as weak as possible. In principle, we will follow Amann’s approach.
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Farwig, R., Galdi, G.P., Sohr, H. (2005). Very Weak Solutions of Stationary and Instationary Navier-Stokes Equations with Nonhomogeneous Data. In: Brezis, H., Chipot, M., Escher, J. (eds) Nonlinear Elliptic and Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 64. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7385-7_7
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