论文标题
消失的扩散极限和一类强制主动标量方程的长时间行为
Vanishing diffusion limits and long time behaviour of a class of forced active scalar equations
论文作者
论文摘要
我们研究了分数laplacian的背景下，抽象的对流扩散方程的属性。两个独立的扩散参数进入系统，一个通过构成定律的漂移速度，一个作为分数拉普拉斯元素的预将因子。我们获得了某些参数制度和限制的存在和收敛。我们研究解决总体问题的长期行为，并证明存在独特的全球吸引子。我们将结果应用于在地球物理流体动力学中产生的两个特定的活性标量方程，即表面准杂质方程和磁化方程。
We investigate the properties of an abstract family of advection diffusion equations in the context of the fractional Laplacian. Two independent diffusion parameters enter the system, one via the constitutive law for the drift velocity and one as the prefactor of the fractional Laplacian. We obtain existence and convergence results in certain parameter regimes and limits. We study the long time behaviour of solutions to the general problem and prove the existence of a unique global attractor. We apply results to two particular active scalar equations arising in geophysical fluid dynamics, namely the surface quasigeostrophic equation and the magnetogeostrophic equation.
