论文标题
Navier-Stokes方程的力以及Koch和Tataru定理
Forces for the Navier-Stokes equations and the Koch and Tataru theorem
论文作者
论文摘要
我们考虑了不可压缩的navier的库奇问题 - 整个空间上的方程$ \ mathbb {r}^3 $，具有初始值$ \ vec u_0 \ in {\ rm bmo}^{ - 1} $（如Koch和Tataru's tataru's tataTaru的理论），而$ \ vec f \ v \ v f = f = \ f = \ cogh v = \ $ \ mathbb {f} $确保在没有初始值的情况下存在温和的解决方案。我们研究了两种解决方案的相互作用，并讨论了在较小的假设下的完整问题（即在存在初始值和强迫项的存在下）的存在。特别是，我们讨论了Koch和Tataru解决方案与Lei-Lin的解决方案之间的相互作用（以$ l^2 \ Mathcal {f}^{ - 1} l^1 $）或在乘数空间$ \ Mathcal {m}（m}（\ dot H^{1/2,1}} _ {1/2,1} _ $ apriper Space $ \ Mathcal {m} _ {t imab x {
We consider the Cauchy problem for the incompressible Navier--Stokes equations on the whole space $\mathbb{R}^3$, with initial value $\vec u_0\in {\rm BMO}^{-1}$ (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 $L^2\mathcal{F}^{-1}L^1$) or solutions in the multiplier space $\mathcal{M}(\dot H^{1/2,1}_{t,x}\mapsto L^2_{t,x})$.
