A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators
A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators
复制标题
作为分数拉普拉斯算子非线性扩散极限的平均场方程
DOI：
10.1007/s00526-013-0613-9
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发表时间：
2013
影响因子：
2.1
通讯作者：
J. Vázquez
中科院分区：
文献类型：
--
作者：
S. Serfaty;J. Vázquez
在涉及分数阶拉普拉斯算子的非线性扩散模型的极限下，我们得到了超导和超流体的“平均场”方程。对于该方程，我们得到了唯一性、普遍界和正则性结果。我们还证明了有限秒矩解和径向解存在一个渐近大时限形，这是一种特殊的自相似解：“初等涡斑”。
In the limit of a nonlinear diffusion model involving the fractional Laplacian we get a “mean field” equation arising in superconductivity and superfluidity. For this equation, we obtain uniqueness, universal bounds and regularity results. We also show that solutions with finite second moment and radial solutions admit an asymptotic large time limiting profile which is a special self-similar solution: the “elementary vortex patch”.