标题： 超导性中出现的平均场演化的适定性 显示英文标题

标题： Well-posedness for mean-field evolutions arising in superconductivity

摘要： 我们建立了对于一类新的类似流体的方程的整体解的存在性，这些方程是在与Serfaty的联合工作中，在某些情况下作为具有钉扎效应并施加电流的二维截面型II超导体中的超电流密度的平均场演化得到的。我们也考虑了一般的涡旋片初始数据，并研究了解的唯一性和正则性性质。对于某些参数选择，所研究的方程与二维浅水流体力学中的所谓湖方程一致，我们的分析随后导致了对粗糙初始数据的新存在性结果。 显示英文摘要

摘要： We establish the existence of a global solution for a new family of fluid-like equations, which are obtained in a joint work with Serfaty in certain regimes as the mean-field evolution of the supercurrent density in a (2D section of a) type-II superconductor with pinning and with imposed electric current. We also consider general vortex-sheet initial data, and investigate the uniqueness and regularity properties of the solution. For some choice of parameters, the equation under investigation coincides with the so-called lake equation from 2D shallow water fluid dynamics, and our analysis then leads to a new existence result for rough initial data.