A note on Monge-Ampere Keller-Segel equation

作者：Huang, Hui^*; Liu, Jian-Guo

来源：Applied Mathematics Letters, 2016, 61: 26-34.

DOI：10.1016/j.aml.2016.05.003

• Chemotaxis
• Polar factorization
• Convex potential
• Brenier map
• Global existence

This note studies the Monge-Ampere Keller-Segel equation in a periodic domain T-d (d >= 2), a fully nonlinear modification of the Keller-Segel equation where the Monge-Ampere equation det(I + del(2)v) = u + 1 substitutes for the usual Poisson equation Delta v = u. The existence of global weak solutions is obtained for this modified equation. Moreover, we prove the regularity in L-infinity (0, T; L-infinity boolean AND W-1,W-1+gamma (T-d)) for some gamma > 0.

• 出版日期2016-11
• 单位清华大学