Further regularity of solutions for almost cubic NLS equation
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Date
2010.
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Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010.
Abstract
This thesis consists of two major parts. In the rst one, we try to give the preliminary local well-posedness results for the ACNLS, and L2 -H1 regularity result which is an easy and straightforward consequence of the equation, since the norm of the gradientof a function can be estimated by di erence quotients. In the second part, we prove some regularity results for ACNLS. First, we prove Hs local well-posedness, where the continuous dependence is weakened; and an improvement of it by obtaining the continuous dependence with an additional condition. At the end, we prove local Xs;b local existence result using Banach xed point theorem, where the interval of existence is not taken to be maximal. The interval depends closely on the arguments of the high-low frequency decomposition.