Mathematica Bohemica, Vol. 147, No. 1, pp. 19-32, 2022
On the radius of spatial analyticity for the higher order nonlinear dispersive equation
Aissa Boukarou, Kaddour Guerbati, Khaled Zennir
Received May 22, 2020. Published online March 16, 2021.
Abstract: In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data $u_0$. The analytic initial data can be extended as holomorphic functions in a strip around the $x$-axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).
Keywords: higher order nonlinear dispersive equation; radius of spatial analyticity; approximate conservation law
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Affiliations: Aissa Boukarou, Kaddour Guerbati, Laboratoire de Mathématiques et Sciences Appliquées, Université de Ghardaia, Zone scientifique, BP 455 Ghardaia, 47000, Algérie, e-mail: boukarou.aissa@univ-ghardaia.dz, guerbati_k@yahoo.com; Khaled Zennir, Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia and Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma, B.P. 401, Guelma 24000 Algérie, e-mail: khaledzennir4@gmail.com
