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Volume 19, Issue 2
The Cauchy Problem of the Modified Kawahara Equation

Guixiang Xu

J. Part. Diff. Eq., 19 (2006), pp. 126-146.

Published online: 2006-05

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  • Abstract

In this paper, we consider the local and global solutions for the modified Kawahara equation with data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data. The techniques to be used are adapted from Kato's smoothing effect and the maximal function (in time) estimate for the free Kawahara operator e^{-ϒ^{t∂^5_x}}.

  • Keywords

Modified Kawahara equation Cauchy problem Littlewood-Paley decomposition Besov space

  • AMS Subject Headings

35Q53 35Q35.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-19-126, author = {Guixiang Xu }, title = {The Cauchy Problem of the Modified Kawahara Equation}, journal = {Journal of Partial Differential Equations}, year = {2006}, volume = {19}, number = {2}, pages = {126--146}, abstract = {

In this paper, we consider the local and global solutions for the modified Kawahara equation with data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data. The techniques to be used are adapted from Kato's smoothing effect and the maximal function (in time) estimate for the free Kawahara operator e^{-ϒ^{t∂^5_x}}.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5324.html} }
TY - JOUR T1 - The Cauchy Problem of the Modified Kawahara Equation AU - Guixiang Xu JO - Journal of Partial Differential Equations VL - 2 SP - 126 EP - 146 PY - 2006 DA - 2006/05 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5324.html KW - Modified Kawahara equation KW - Cauchy problem KW - Littlewood-Paley decomposition KW - Besov space AB -

In this paper, we consider the local and global solutions for the modified Kawahara equation with data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data. The techniques to be used are adapted from Kato's smoothing effect and the maximal function (in time) estimate for the free Kawahara operator e^{-ϒ^{t∂^5_x}}.

Guixiang Xu . (2006). The Cauchy Problem of the Modified Kawahara Equation. Journal of Partial Differential Equations. 19 (2). 126-146. doi:
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