ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID(Ⅰ)

On the well posedness of initial value problem for euler equations of incompressible inviscid fluid (I)

The ill posed initial value problem of the Euler equations and the formal solvability of ill posed problem based on stratification theory are discussed. For some ill posed initial value problems, the existence conditions of formal solutions and the methods of how to construct a formal solution are given. Finally, an example is given to discuss the ill posedness of the initial value problem on hyper plane {t=0} in R⁴, and explain that the problem has more than one solution. Foundation item: the National Natural Science Foundation of China (19971054) Biography: Shen Zhen (1977−)