On the Well Posedness of Initial Value Problem for Euler Equations of Incompressible Inviscid Fluid(Ⅰ)
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摘要: 以分层理论为基础,讨论了Euler方程不适定的初值问题以及不适定问题的形式可解性,并给出了某些不适定初值问题存在形式解的条件与计算方法。特别讨论了R4中的超平面{t=0}上初值问题的适定性并给出了存在不唯一解的例证。Abstract: The ill posed initial value problem of the Euler Equations and the formal solvability of ill posed problem based on stratification theory is 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}⊆R4 and explain that the problem has more than one solution.
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Key words:
- Euler equation /
- ill posed problem /
- formal solution /
- equation secondaire
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