论文标题
在一类具有小扩散参数的强制活动标量方程
On a class of forced active scalar equations with small diffusive parameters
论文作者
论文摘要
模拟流体行为的许多方程都是从包含多个物理力的系统中得出的。当方程以适合这种情况物理的非维形式编写时，所得的部分微分方程通常包含几个小参数。我们研究了一类称为主动标量方程的一般PDES，在特定参数方程中产生了某些已知的流体运动模型。我们解决了有关该通用类别解决方案解决方案的各种数学问题，包括几个扩散参数的消失限制。
Many equations that model fluid behaviour are derived from systems that encompass multiple physical forces. When the equations are written in non dimensional form appropriate to the physics of the situation, the resulting partial differential equations often contain several small parameters. We study a general class of such PDEs called active scalar equations which in specific parameter regimes produce certain well known models for fluid motion. We address various mathematical questions relating to well-posedness, regularity and long time behaviour of the solutions to this general class including vanishing limits of several diffusive parameters.
