TY - JOUR
TI - Variational principle for an incompressible flow
AU - Wu Yue
AU - Feng Guang-Qing
JN - Thermal Science
PY - 2023
VL - 27
IS - 3
SP - 2039
EP - 2047
PT - Article
AB - This paper gives a general approach to the inverse problem of calculus of  variations. The 2-D Euler equations of incompressible flow are used as an  example to show how to derive a variational formulation. The paper begins  with ideal Laplace equation for its potential flow without vorticity, which  admits the Kelvin 1849 variational principle. The next step is to assume a  small vorticity to obtain an approximate variational formulation, which is  then amended by adding an additional unknown term for further determined,  this process leads to the well-known semi-inverse method. Lagrange crisis is  also introduced, and some methods to solve the crisis are discussed