Spatial asymptotic expansion of the Euler equation

• Online Access: http://hdl.handle.net/2047/D20328768

In this dissertation we study the Euler equation in dimension 2 and higher. We show that the Euler equation is locally well-posed in the space of spatially asymptotic functions. Furthermore, we prove that the 2d Euler equation is globally well-posed in the corresponding asymptotic space. We discuss how the Euler equation preserves certain function spaces that have asymptotic expansions. These asymptotic function spaces are known to have asymptotic terms that include logarithms. However, we show that structurally simpler spaces without log terms are also preserved by the Euler equation. In 2 dimensional fluid flow the complex structure can be used to find such smaller function spaces without log terms.--Author's abstract