# Local Solution to the Multi-layer KPZ Equation

@article{Chandra2019LocalST, title={Local Solution to the Multi-layer KPZ Equation}, author={A. Chandra and D. Erhard and H. Shen}, journal={Journal of Statistical Physics}, year={2019}, volume={175}, pages={1080-1106} }

In this article we prove local well-posedness of the system of equations $$\partial _t h_{i}= \sum _{j=1}^{i}\partial _x^2 h_{j}+ (\partial _x h_{i})^2 + \xi $$∂thi=∑j=1i∂x2hj+(∂xhi)2+ξ on the circle where $$1\le i\le N$$1≤i≤N and $$\xi $$ξ is a space-time white noise. We attempt to generalize the renormalization procedure which gives the Hopf-Cole solution for the single layer equation and our $$h_1$$h1 (solution to the first layer) coincides with this solution. However, we observe that… CONTINUE READING

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