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- W4378194655 abstract "We consider the Cauchy problem for the incompressible Navier--Stokes equations on the whole space $mathbb{R}^3$, with initial value $vec u_0in {rm BMO}^{-1}$ (as in Koch and Tataru's theorem) and with force $vec f=Div mathbb{F}$ where smallness of $mathbb{F}$ ensures existence of a mild solution in absence of initial value. We study the interaction of the two solutions and discuss the existence of global solution for the complete problem (i.e. in presence of initial value and forcing term) under smallness assumptions. In particular, we discuss the interaction between Koch and Tataru solutions and Lei-Lin's solutions (in $L^2mathcal{F}^{-1}L^1$) or solutions in the multiplier space $mathcal{M}(dot H^{1/2,1}_{t,x}mapsto L^2_{t,x})$." @default.
- W4378194655 created "2023-05-26" @default.
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- W4378194655 date "2023-05-25" @default.
- W4378194655 modified "2023-10-17" @default.
- W4378194655 title "Forces for the Navier–Stokes Equations and the Koch and Tataru Theorem" @default.
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- W4378194655 doi "https://doi.org/10.1007/s00021-023-00788-6" @default.
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