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Type of Document	Dissertation
Author	Schlotthauer-Hannah, Heather Dawn
Author's Email Address	hhannah@ecok.edu
URN	etd-04202007-135742
Title	WELL-POSEDNESS AND REGULARITY FOR A HIGHER ORDER PERIODIC mKdV EQUATION
Degree	Doctor of Philosophy
Department	Mathematics
Advisory Committee	Advisor Name Title Alex Himonas Committee Member
Keywords	Partial Differential equations mKdV equation higher order dispersion equations
Date of Defense	2007-03-22
Availability	mixed
Abstract We consider the higher order mKdV equation, so that we are examining those equations with a higher dispersion term of the order m, where m is odd and larger than 3. The corresponding periodic Cauchy problem is in fact well-posed in Sobolev spaces for all s ge 1/2. We then show that the solution to the periodic Cauchy problem for this higher order equation with analytic initial data is analytic in the space variable x at any fixed time t near time zero. However, while this analyticity is not guaranteed in t, the solution does have Gevrey-m regularity with respect to the time variable t.
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