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

摘要

The ill posed initial value problem of the Euler equations and the formalsolvability of ill posed problem based on stratification theory are discussed. For some illposed initial value problens , the existence conditions of formal solutions and the methods ofhow to cons truct a formal solution are given. Finally, an example is given to discuss the illposedness of the initial value problem on hyper plane { t = 0 } in R4, and explain that theproblem has more than one solution.