Titlebook: Mathematical Theory of Incompressible Nonviscous Fluids; Carlo Marchioro,Mario Pulvirenti Book 1994 Springer-Verlag New York, Inc. 1994 De

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General Considerations on the Euler Equation,This chapter has an introductory nature, wherein we discuss the fundamental equations describing the motion of an incompressible nonviscous fluid and establish some elementary properties.

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Construction of the Solutions,In this chapter we study the problem of the existence and uniqueness of the solutions of the Euler equation. The Euler equation, deduced and discussed in the previous chapter, is a nonlinear equation. This implies that the construction of its solutions may be a nontrivial task. In this chapter we study this problem.

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Stability of Stationary Solutions of the Euler Equation,In this chapter we investigate some qualitative properties of solutions of the Euler equation and, in particular, we give sufficient conditions for the stability of stationary flows and discuss some instabilities.

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The Vortex Model,In this chapter we introduce and study the vortex model. Its relation with the Euler equation is investigated in some detail. Finally, we also discuss three-dimensional models.

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Approximation Methods,In this chapter we introduce the spectral and the vortex methods as finite-dimensional approximation schemes for the Euler equation in two dimensions. We discuss the convergence of these approximations to the solutions.

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