“天山论坛”学术报告

题目：A solution formula for the incompressible Navier-Stokes equation

报告人：陈泽乾，中科院武汉物理与数学所研究员、博士生导师

时间：12月1日 11:00-13:00时

地点：2号楼206

摘要：We  will report a framework that introduces an infinite linear hierarchy  for the homogeneous, incompressible three-dimensional Navier-Stokes  equation. The Cauchy problem of the hierarchy with a factorized  divergence-free initial datum is shown to be equivalent to that of the  incompressible Navier-Stokes equation in $\mathcal{H}^1.$ This allows us  to present an explicit formula for solutions to the incompressible  Navier-Stokes equation under consideration. The formula obtained is an  expansion in terms of binary trees encoding the collision histories of  the ``particles" in a concise form. Precisely, each term in the  summation of $n$ ``particles" collision is expressed by a $n$-parameter  singular integral operator with an explicit kernel in Fourier space,  describing a kind of processes of two-body interaction of $n$  ``particles". Therefore, this formula is a physical expression for the  solutions of the incompressible Navier-Stokes equation.