The periodic Cauchy problem of the modified Hunter-Saxton equation |
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Authors: | Feride Ti?lay |
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Institution: | (1) Department of Mathematics, University of New Orleans, Lakefront, New Orleans, LA 70148, USA |
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Abstract: | We prove that the periodic initial value problem for the modified Hunter-Saxton equation is locally well-posed for initial
data in the space of continuously differentiable functions on the circle and in Sobolev spaces
when s > 3/2. We also study the analytic regularity (both in space and time variables) of this problem and prove a Cauchy-Kowalevski
type theorem. Our approach is to rewrite the equation and derive the estimates which permit application of o.d.e. techniques
in Banach spaces. For the analytic regularity we use a contraction argument on an appropriate scale of Banach spaces to obtain
analyticity in both time and space variables. |
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Keywords: | 35Q58 35Q53 35A10 |
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