Abstract: The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some representative initial or boundary value problem, thus the structure of solution space for local (exact) solution of the Euler equations is determined.Moreover the computation formulas of the analytical solution of the well-posed problem are also given.

Key words: Euler equation, initial or boundary value problem, well-posedness, stratification theory