论文标题
在关键函数空间中，全球半空间问题的全局良好性是限制案例
Global well-posedness of the half space problem of the Navier-Stokes equations in critical function spaces of limiting case
论文作者
论文摘要
在本文中，我们研究了半空间的Navier-Stokes方程的初始值问题。令螺线管初始速度在功能空间中给出$ \ dot {b} _ {p \ infty，0}^{-1 + n/p}（{\ m athbb r}^n _ +）$ for $ \ frac {n} 3 <p <n $。我们证明了l^\ infty（0，\ infty; \ dot b^{ - 1 +n/p} _ {p \ infty}（{\ Mathbb r}^n _ +）$，当给定初始速度的功能空间$时\ dot {b} _ {p \ infty，0}^{ - 1 + n/p}（{\ mathbb r}^n _ +）$，其中$ \ frac {n} 3 <p <n $。
In this paper, we study the initial-boundary value problem of the Navier-Stokes equations in half-space. Let a solenoidal initial velocity be given in the function space $ \dot{B}_{p\infty,0}^{ -1 + n/p}({\mathbb R}^n_+)$ for $ \frac{n}3< p < n$. We prove the global in time existence of weak solution $u\in L^\infty(0,\infty; \dot B^{-1 +n/p}_{p\infty}({\mathbb R}^n_+))$, when the given initial velocity has small norm in function space $ \dot{B}_{p\infty,0}^{-1 + n/p} ({\mathbb R}^n_+)$, where $ \frac{n}3< p< n$.
