American Institute of Mathematical Sciences

Advanced
December  2006, 5(4): 887-905. doi: 10.3934/cpaa.2006.5.887

Cauchy problem for the fifth order Kadomtsev-Petviashvili (KPII) equation

Pedro Isaza 1, , Juan López 2, and  Jorge Mejía 1,

1. 

Universidad Nacional de Colombia, Sede Medellín, A.A. 3840, Medellín, Colombia, Colombia
2. 

Universidad de Pamplona, Pamplona, Colombia

Received  November 2005 Revised  March 2006 Published  September 2006

It is proved that the initial value problem for the fifth order Kadomtsev-Petviashvili (KPII) equation is locally well-posed in the anisotropic Sobolev spaces $H^{s_1,s_2}( \mathbb R^2) $ with $s_1$>$-\frac{5}{4}$ and $s_2\geq 0,$ and globally well-posed in $H^{s,0}(\mathbb R^2) $ with $s$>$-\frac{4}{7}.$
Keywords: Nonlinear dispersive equations, local solutions, global solutions..
Mathematics Subject Classification: Primary: 35Q53; Secondary: 37K0.
Citation: Pedro Isaza, Juan López, Jorge Mejía. Cauchy problem for the fifth order Kadomtsev-Petviashvili (KPII) equation. Communications on Pure & Applied Analysis, 2006, 5 (4) : 887-905. doi: 10.3934/cpaa.2006.5.887
[1]

Hongqiu Chen, Jerry L. Bona. Periodic traveling--wave solutions of nonlinear dispersive evolution equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 4841-4873. doi: 10.3934/dcds.2013.33.4841
[2]

Jerry L. Bona, Laihan Luo. More results on the decay of solutions to nonlinear, dispersive wave equations. Discrete & Continuous Dynamical Systems - A, 1995, 1 (2) : 151-193. doi: 10.3934/dcds.1995.1.151
[3]

Fabrício Cristófani, Ademir Pastor. Nonlinear stability of periodic-wave solutions for systems of dispersive equations. Communications on Pure & Applied Analysis, 2020, 19 (10) : 5015-5032. doi: 10.3934/cpaa.2020225
[4]

Zuzana Došlá, Mauro Marini, Serena Matucci. Global Kneser solutions to nonlinear equations with indefinite weight. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3297-3308. doi: 10.3934/dcdsb.2018252
[5]

Makoto Nakamura. Remarks on global solutions of dissipative wave equations with exponential nonlinear terms. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1533-1545. doi: 10.3934/cpaa.2015.14.1533
[6]

Hiroshi Takeda. Global existence of solutions for higher order nonlinear damped wave equations. Conference Publications, 2011, 2011 (Special) : 1358-1367. doi: 10.3934/proc.2011.2011.1358
[7]

Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar. On the local and global existence of solutions to 1d transport equations with nonlocal velocity. Networks & Heterogeneous Media, 2019, 14 (3) : 471-487. doi: 10.3934/nhm.2019019
[8]

Xiaojie Hou, Yi Li. Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 681-701. doi: 10.3934/dcds.2006.15.681
[9]

Thomas Duyckaerts, Carlos E. Kenig, Frank Merle. Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1275-1326. doi: 10.3934/cpaa.2015.14.1275
[10]

Honglv Ma, Jin Zhang, Chengkui Zhong. Global existence and asymptotic behavior of global smooth solutions to the Kirchhoff equations with strong nonlinear damping. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 4721-4737. doi: 10.3934/dcdsb.2019027
[11]

Nakao Hayashi, Seishirou Kobayashi, Pavel I. Naumkin. Nonlinear dispersive wave equations in two space dimensions. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1377-1393. doi: 10.3934/cpaa.2015.14.1377
[12]

Tong Tang, Hongjun Gao. Local strong solutions to the compressible viscous magnetohydrodynamic equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1617-1633. doi: 10.3934/dcdsb.2016014
[13]

Xiaoli Li, Dehua Wang. Global solutions to the incompressible magnetohydrodynamic equations. Communications on Pure & Applied Analysis, 2012, 11 (2) : 763-783. doi: 10.3934/cpaa.2012.11.763
[14]

Peter Constantin, Gregory Seregin. Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1185-1196. doi: 10.3934/dcds.2010.26.1185
[15]

Xie Li, Zhaoyin Xiang. Existence and nonexistence of local/global solutions for a nonhomogeneous heat equation. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1465-1480. doi: 10.3934/cpaa.2014.13.1465
[16]

Yucheng Bu, Yujun Dong. Existence of solutions for nonlinear operator equations. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4429-4441. doi: 10.3934/dcds.2019180
[17]

Takahiro Hashimoto. Nonexistence of global solutions of nonlinear Schrodinger equations in non star-shaped domains. Conference Publications, 2007, 2007 (Special) : 487-494. doi: 10.3934/proc.2007.2007.487
[18]

Mingyou Zhang, Qingsong Zhao, Yu Liu, Wenke Li. Finite time blow-up and global existence of solutions for semilinear parabolic equations with nonlinear dynamical boundary condition. Electronic Research Archive, 2020, 28 (1) : 369-381. doi: 10.3934/era.2020021
[19]

Linghai Zhang. Decay estimates with sharp rates of global solutions of nonlinear systems of fluid dynamics equations. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2181-2200. doi: 10.3934/dcdss.2016091
[20]

Bilgesu A. Bilgin, Varga K. Kalantarov. Non-existence of global solutions to nonlinear wave equations with positive initial energy. Communications on Pure & Applied Analysis, 2018, 17 (3) : 987-999. doi: 10.3934/cpaa.2018048

2019 Impact Factor: 1.105

Tools

Metrics

  • PDF downloads (40)
  • HTML views (0)
  • Cited by (9)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences