Local solution to the multi-layer KPZ equation

Ajay Chandra, Dirk Erhard, Hao Shen

In this article we prove local well-posedness of the system of equations ${\partial }_t{h}_i={\sum }_{j=1}^i{\partial }_x^2{h}_i+({\partial }_x{h}_i{)}^2+\xi$ on the circle where $1\leq i…