This thesis investigates questions of uniqueness in the theory of Compressible flow. First, various uniqueness theorems for compressible flow are reviewed in an expository manner. Roughly, these theorems state that fluid motion in a bounded region Ω = Ω(t) is uniquely determined by its initial data together along with certain boundary conditions. Next, this analysis is extended to magnetohydrodynamic flows and uniqueness theorems are given for a variety of possible cases. The basic question in all these theorems is the determination of appropriate boundary conditions. The proofs are by energy estimates. / Science, Faculty of / Mathematics, Department of / Graduate