caa a22 4500 606194444 CHVBK 20210128100914.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00030-015-0317-2 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0317-2 Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains [Elektronische Daten] [Reinhard Farwig, Paul Riechwald] We consider the instationary Navier-Stokes system in general unbounded domains $${\Omega \subset \mathbb{R}^{n}}$$ Ω ⊂ R n , $${n\geq 3}$$ n ≥ 3 , with smooth boundary and construct by the Fujita-Kato method mild solutions $${u\in L^{\infty}(0,T; \tilde{L}^{n}(\Omega))}$$ u ∈ L ∞ ( 0 , T ; L ~ n ( Ω ) ) with initial value $${u_0\in\tilde{L}^{n}(\Omega)}$$ u 0 ∈ L ~ n ( Ω ) . Here the classical $${L^n(\Omega)}$$ L n ( Ω ) -space is replaced by $${\tilde{L}^n(\Omega)}$$ L ~ n ( Ω ) where for q>2 the space $${\tilde{L}^q}$$ L ~ q is defined by $${L^q\cap L^2}$$ L q ∩ L 2 . Moreover, for suitable initial values we identify mild solutions in $${L^\infty(0,T;\tilde{L}^n(\Omega))}$$ L ∞ ( 0 , T ; L ~ n ( Ω ) ) with very weak solutions in Serrin's class $${L^r (0,T;\tilde{L}^q(\Omega))}$$ L r ( 0 , T ; L ~ q ( Ω ) ) where $${\frac{2}{r} + \frac{n}{q} =1}$$ 2 r + n q = 1 , $${2< r < \infty}$$ 2 < r < ∞ . Springer Basel, 2015 Navier-Stokes equations nationallicence Fujita-Kato method nationallicence Mild solutions nationallicence Very weak solutions nationallicence General unbounded domains nationallicence Spaces $${\tilde{L}^{q}(\Omega)}$$ L ~ q ( Ω ) nationallicence Farwig Reinhard Fachbereich Mathematik, Technische Universität Darmstadt, 64289, Darmstadt, Germany aut Riechwald Paul Fachbereich Mathematik, Technische Universität Darmstadt, 64289, Darmstadt, Germany aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1143-1165 1021-9722 22:5<1143 2015 22 30 https://doi.org/10.1007/s00030-015-0317-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0317-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Farwig Reinhard Fachbereich Mathematik, Technische Universität Darmstadt, 64289, Darmstadt, Germany aut NATIONALLICENCE 700 1- Riechwald Paul Fachbereich Mathematik, Technische Universität Darmstadt, 64289, Darmstadt, Germany aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1143-1165 1021-9722 22:5<1143 2015 22 30