The asymptotic behaviour of subcritical dissipative quasi-geostrophic equations
The asymptotic behaviour of subcritical dissipative quasi-geostrophic equations
复制标题
DOI：
10.1088/0951-7715/21/5/006
复制
发表时间：
2008-05
期刊：
影响因子：
1.7
通讯作者：
J. Carrillo;L. Ferreira
中科院分区：
文献类型：
--
作者：
J. Carrillo;L. Ferreira
本文给出了准地转方程在亚临界区的渐近行为的完整描述。我们首先证明它的解渐近简化为t → ∞。更准确地说，当t → ∞时，解表现为一个特定的自相似解，由质量归一化，当初始数据属于。另一方面，我们证明了在这个空间中，当t → ∞时，具有初始数据的解衰减到零.无论初始条件的大小如何，都可以得到所有结果。
In this work, we give a complete description of the asymptotic behaviour of quasi-geostrophic equations in the subcritical range . We first show that its solutions simplify asymptotically as t → ∞. More precisely, solutions behave as a particular self-similar solution normalized by the mass as t → ∞ and when the initial data belong to . On the other hand, we show that solutions with initial data in decay towards zero as t → ∞ in this space. All results are obtained regardless of the size of the initial condition.