Well-posedness and regularity of the fifth order Kadomtsev–Petviashvili I equation in the analytic Bourgain spaces

Boukarou, Aissa; Zennir, Khaled; Guerbati, Kaddour; Svetlin, G. G.

doi:10.1007/s11565-020-00340-8

Cited by 9 publications

(3 citation statements)

References 16 publications

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“…Appl. 2021, 26, 75. https://doi.org/10.3390/mca26040075 https://www.mdpi.com/journal/mca which is known as a model for long waves in a viscous fluid flowing down an inclined plane; see [1][2][3][4][5][6][7][8]. It is considered as a particular case of the Benney-Lin equation:…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Spatial Analyticity of Solutions to Korteweg–de Vries Type Equations

Bouhali

Moumen

Tajer

et al. 2021

MCA

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The Korteweg–de Vries equation (KdV) is a mathematical model of waves on shallow water surfaces. It is given as third-order nonlinear partial differential equation and plays a very important role in the theory of nonlinear waves. It was obtained by Boussinesq in 1877, and a detailed analysis was performed by Korteweg and de Vries in 1895. In this article, by using multi-linear estimates in Bourgain type spaces, we prove the local well-posedness of the initial value problem associated with the Korteweg–de Vries equations. The solution is established online for analytic initial data w0 that can be extended as holomorphic functions in a strip around the x-axis. A procedure for constructing a global solution is proposed, which improves upon earlier results.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Spatial Analyticity of Solutions to Korteweg–de Vries Type Equations

Bouhali

Moumen

Tajer

et al. 2021

MCA

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“…There is another method in this direction, we mention the works by A. Boukarou et al in the next series of papers [7,8,9,10,11,12,22]. Motivated by the previouse results, we consider our main ptoblem with initial data are analytic on a band in the complex plane and obtained solution for all time.…”

Section: Introductionmentioning

confidence: 99%

Spatial analyticity of solutions for a coupled system of generalized KdV equations

Atmani¹,

Boukarou²,

Benterki³

et al. 2022

Preprint

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“…There is another method in this direction; we mention the works by A. Boukarou et al in the next series of papers [4,[14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Spatial analyticity of solutions for a coupled system of generalized KdV equations

Atmani,

Boukarou,

Benterki

et al. 2024

Math Methods in App Sciences

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We consider the well‐posedness of a coupled system for generalized Korteweg–de Vries (S‐gKdV) where and the initial data are analytic in a strip and then the solutions of S‐gKdV continue to be analytic in a strip the width of which will decrease as time goes to , by using the standard contraction method in analytic Bourgain space. Besides, we obtain algebraic lower bounds on the decreasing rate of the uniform radius of analyticity of the solutions.

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Well-posedness and regularity of the fifth order Kadomtsev–Petviashvili I equation in the analytic Bourgain spaces

Abstract: We show that the fifth-order Kadomtsev-Petviashvili II equation is globally well-posed in an anisotropic Gevrey space, which complements earlier results on the well-posedness of this equation in anisotropic Sobolev spaces. 2010 Mathematics Subject Classification. 35Q35, 35Q53.

Cited by 9 publications

References 16 publications

Spatial Analyticity of Solutions to Korteweg–de Vries Type Equations

Spatial Analyticity of Solutions to Korteweg–de Vries Type Equations

Spatial analyticity of solutions for a coupled system of generalized KdV equations

Spatial analyticity of solutions for a coupled system of generalized KdV equations

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