论文标题
关于半线性抛物线系统解决方案的分析性的半径
On the radius of analyticity of solutions to semi-linear parabolic systems
论文作者
论文摘要
我们研究了分析性〜$ r（t）$的半径，这是针对比例不变半线性抛物线方程系统的强大解决方案。众所周知，在初始时间接近〜$ r（t）t^{ - \ frac12} $以正常数为界。在本文中，我们证明了〜$ \ displayStyle \ liminf_ {t \ rightArrow 0} r（t）t^{ - \ frac12} = \ infty $，并且假设初始数据的规律性更高，我们获得了改进的改进的下限下限近距离近距离零。作为一个应用程序，我们证明，对于任何全局解决方案〜$ u \ in c（[0，\ infty）; h^{\ frac12}（\ r^3））$的navier-stokes方程，其中保留〜$ \ displayStyle \ liminf_ {t \ rightArrow \ rightArrow \ infty} r（t）t^{ - \ frac12} = \ infty $。
We study the radius of analyticity~$R(t)$ in space, of strong solutions to systems of scale-invariant semi-linear parabolic equations. It is well-known that near the initial time,~$R(t)t^{-\frac12}$ is bounded from below by a positive constant. In this paper we prove that~$\displaystyle\liminf_{t\rightarrow 0} R(t)t^{-\frac12}= \infty$, and assuming higher regularity for the initial data, we obtain an improved lower bound near time zero. As an application, we prove that for any global solution~$u\in C([0,\infty); H^{\frac12}(\R^3))$ of the Navier-Stokes equations, there holds~$\displaystyle\liminf_{t\rightarrow \infty} R(t)t^{-\frac12}= \infty$.
