中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：单敏捷 副教授（中央民族大学理学院）
题 目：Low regularity conservation laws for the fifth-order modified KdV equations in Besov spaces
时 间：2023.03.02（星期四）14:30-16:30
地 点：数学院南楼N208
摘 要：We get a priori estimates for the fifth-order modified KdV equations in Besov spaces with low regularity which cover the full subcritical range. These estimates are obtained from the power series expansion of the perturbation determinant associated to the Lax pair. More precisely, we get the global in time bounds of the $B^s_{2,r}$ norm of the solution for $-1/2< s < 1$, $1\leq r \leq \infty$. Then we can obtain the sharp global well-posedness in $H^s$ for $s\geq 3/4$, which is the minimal regularity threshold for which the well-posedness problem can be solved via the contraction principle.
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