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• W2912887964 abstract "It is well known that there exists a unique local-in-time strong solution u of the initial boundary value problem for the Navier–Stokes system in a three-dimensional smooth bounded domain when the initial velocity $$u_0$$ belongs to critical Besov spaces. A typical space is $$B=B^{-1+3/q}_{q,s}$$ with $$3<q<infty $$, $$2<s<infty $$ satisfying $$2/s+3/q le 1$$ or $$B=mathring{B}^{-1+3/q}_{q,infty }$$. In this paper, we show that the solution u is continuous in time up to initial time with values in B. Moreover, the solution map $$u_0mapsto u$$ is locally Lipschitz from B to $$Cleft( [0,T];Bright) $$. This implies that in the range $$3<q<infty $$, $$2<sle infty $$ with $$3/q +2/s le 1$$ the problem is well posed which is in strong contrast to norm inflation phenomena in the space $$B^{-1}_{infty ,s}$$, $$1le s <infty $$ proved in the last years for the whole space case." @default.
• W2912887964 created "2019-02-21" @default.
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• W2912887964 date "2019-02-07" @default.
• W2912887964 modified "2023-10-06" @default.
• W2912887964 title "On the continuity of the solutions to the Navier–Stokes equations with initial data in critical Besov spaces" @default.
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• W2912887964 doi "https://doi.org/10.1007/s10231-019-00824-1" @default.
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