In this paper, we study a non-local coupled system that arises in the theory of dislocations densities dynamics. Based on a new gradient entropy estimate in \(L \log L\) space, we prove the global existence of a continuous solution. The approach is made by adding a viscosity term and passing to the limit for vanishing viscosity. A comparison principle with respect to time is used for proving uniqueness of the solution for the local problem.

中文翻译：

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建模位错密度的非局部耦合系统连续解的存在性和唯一性

在本文中，我们研究了在位错密度动力学理论中出现的非局部耦合系统。基于\（L \ log L \）空间中的新梯度熵估计，我们证明了连续解的整体存在性。该方法是通过添加粘度项并达到消失粘度的极限来实现的。关于时间的比较原理用于证明局部问题的解的唯一性。