论文标题
粘性轴对称流体没有漩涡
Time-Asymptotic Study of a Viscous Axisymmetric Fluid without Swirl
论文作者
论文摘要
我们研究了整个空间中三二维Navier-Stokes方程的轴对称溶液的长期行为。假设最初的涡度已经充分局部，则在解决方案的渐近膨胀中明确计算涡度和速度场中的主要术语。特别是，我们根据初始数据的空间定位确定最佳的时间衰减率。我们的方法依赖于线性化演化方程式的准确$ l^p $ - $ l^q $估计值及其在自相似变量中的泰勒扩展。
We study the long-time behaviour of axisymmetric solutions without swirl for the threedimensional Navier-Stokes equations in the whole space. Assuming that the initial vorticity is sufficiently localised, we compute explicitly the leading terms in the asymptotic expansion of the solution, both for the vorticity and the velocity field. In particular, we identify optimal temporal decay rates depending on the spatial localisation of the initial data. Our approach relies on accurate $L^p$-$L^q$ estimates for the linearised evolution equation and its Taylor expansion in self-similar variables.
