Philip MorrisonLINEAR INSTABILITY FOR INCOMPRESSIBLE INVISCID FLUID FLOWS: TWO CLASSES OF

I am indebted to several people for their help and support leading up to the completion of this dissertation. First, I wish to thank Boris Kunin for convincing me to become a mathematician and for the countless hours of discussion that prepared me for graduate school in mathematics. I would also like to thank Misha Vishik, not only for introducing me to some very interesting mathematics, but also for his dedication as my advisor. Misha always encouraged me to be my own mathematician and kept me from making any terrible mistakes along the way. Several other members of the department here at UT have graciously shared their time and wisdom to provided me with support both academic and non-academic throughout my graduate career. I especially wish to thank Irene Gamba, Karen Uhlenbeck and Bill Beckner. My fellow graduate students have been excellent collegues – in particular I would like to thank Tim Blass for all of the helpful mathematical discussions. I am grateful to my dad for his enthusiastic encouragement of all my scientific pursuits, and to my mom for showing me what it is to be a woman totally confident in her intellectual abilities. I am also grateful to Brian, Pippa, Adri and Brandy for being truly amazing friends. Finally, I would like to v express deepest gratitude to Mike for his patience and understanding, which have made it possible for me to pursue a career in mathematics. vi LINEAR INSTABILITY FOR INCOMPRESSIBL