Geodesic
On the radius of spatial analyticity for the higher order nonlinear dispersive equation
Mathematica Bohemica, Tome 147 (2022) no. 1, pp. 19-32
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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).
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).
DOI : 10.21136/MB.2021.0096-20
Classification : 35B65, 35C07, 35E15, 35Q53
Keywords: higher order nonlinear dispersive equation; radius of spatial analyticity; approximate conservation law 
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Boukarou, Aissa; Guerbati, Kaddour; Zennir, Khaled. On the radius of spatial analyticity for the higher order nonlinear dispersive equation. Mathematica Bohemica, Tome 147 (2022) no. 1, pp. 19-32. doi: 10.21136/MB.2021.0096-20

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