数学
欧拉公式
空格(标点符号)
欧拉系统
数学分析
纯数学
数学物理
欧拉方程
计算机科学
操作系统
作者
Young-Pil Choi,Jinwook Jung,Junha Kim
标识
DOI:10.1016/j.jde.2024.04.025
摘要
In this paper, we present a refined framework for the global-in-time well-posedness theory for the pressureless Euler–Navier–Stokes system and the optimal temporal decay rates of certain norms of solutions. Here the coupling of two systems, pressureless Euler system and incompressible Navier–Stoke system, is through the drag force. We construct the global-in-time existence and uniqueness of regular solutions for the pressureless Euler–Navier–Stokes system without using a priori large time behavior estimates. Moreover, we seek for the optimal Sobolev regularity for the solutions. Concerning the temporal decay for solutions, we show that the fluid velocities exhibit the same decay rate as that of the heat equations. In particular, our result provides that the temporal decay rate of difference between two velocities, which is faster than the fluid velocities themselves, is at least the same as the second-order derivatives of fluid velocities.
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