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Propagation of Regularity and Persistence of Decay for Fifth Order Dispersive Models

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Abstract

This paper considers the initial value problem for a class of fifth order dispersive models containing the fifth order KdV equation

$$\begin{aligned} \partial _tu - \partial _x^5u -30u^2\partial _xu + 20\partial _xu\partial _x^2u + 10u\partial _x^3u = 0. \end{aligned}$$

The main results show that regularity or polynomial decay of the data on the positive half-line yields regularity in the solution for positive times.

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Acknowledgments

A portion of this work was completed while J.S was visiting the Department of Mathematics at the University of California, Santa Barbara whose hospitality he gratefully acknowledges. The authors thank Professor Gustavo Ponce for giving us valuable comments. J.S is partially supported by JSPS, Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation and by MEXT, Grant-in-Aid for Young Scientists (A) 25707004.

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  1. Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan

    Jun-Ichi Segata

  2. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA

    Derek L. Smith

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  1. Jun-Ichi Segata
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  2. Derek L. Smith
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Correspondence to Derek L. Smith.

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Segata, JI., Smith, D.L. Propagation of Regularity and Persistence of Decay for Fifth Order Dispersive Models. J Dyn Diff Equat 29, 701–736 (2017). https://doi.org/10.1007/s10884-015-9499-x

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