This is a joint course with NCTS/TPE aimed at interdisciplinary research between
mathematics and atmospheric /oceanic sciences. The group of the lecturers includes at least
Professors Hung-Chi Kuo (NTU), Ching-Hsiao Cheng (NCU), Chi-Hin Chan (NCTU),
Chia-Chieh Chu (NTHU) and Ming-Cheng Shiue (NCU). There are three main parts of this
course.
1> Mathematical Theory : We first review the basic mathematical theory of Navier-Stokes
equations in the first a few weeks. Then we introduce the Littlewood-Paley theory. Then it
follows with the applications to incompressible Euler equations and the Cauchy problems of
the Boussinesq equations. Meanwhile, from time to time, we present the recent advanced
results in this field.
2> Numerical Simulation : We introduce several very useful numerical methods to do
simulations for fluid problems. One of the key methods to study the incompressible fluids is
the so-called finite volume method. Besides introducing the scheme, we will help students to
do implementation as well. We expect every student who joins this program would eventually
get himself/herself familiar with some useful numerical schemes.
3> Interdisciplinary part: We will invite professors from atmospheric sciences and oceanic
sciences to give short courses to introduce the main ingredients in their disciplines and point
out the connections between mathematics.