3月16日(金) 13:30 -- 14:30 申 東雨 (大韓民国, ソウル国立大学)
``The Helmholtz and Leray decompositions and their applications
to Maxwell's equations.''
＜研究発表要旨＞
In 1858 Hermann von Helmholtz introduced the idea of decomposing a fluid
vector field $(u,v,w)$ as a sum of $\nabla p + \nabla\times (L,M,N).$
Since then, the theory of Helmholtz decomposition of vector field has been
elaborated by many mathematicians and now it becomes one of the most
fundamental and useful theory in the analysis of solutions of partial
differential equations arising from fluid/solid mechanics and
electromagnetics.
In this talk we will review recent results on the Helmholtz and Leray
decompositions for vector fields. Under various assumptions on
$\Omega\in \mathbb R^d,$ for $d =2,3,$ we will first look at the classical
decomposition theory of $[L^2(\Omega)]^d$, and then the corresponding
theory of $[L^r(\Omega)]^d, 1