Persistence properties for the two-component Novikov equation in weighted L^p spaces

References

• Popowicz Z . Double extended cubic peakon equation. Phys Lett A. 2015;379:1240–1245.
   Web of Science ®Google Scholar
• Luo W , Yin Z . Local well-posedness and blow up for two-component Novikov system in the critical Besov space. Nonlinear Anal. 2015;122:1–22.
   Web of Science ®Google Scholar
• Novikov V . Generalizations of Camassa--Holm equation. J Phys A. 2009;42:342002. 14 p.
   Google Scholar
• Hone ANW , Wang J . Integrable peakon equations with cubic nonlinearity. J Phys A. 2008;41:4359–4380.
   Google Scholar
• Jiang Z , Ni L . Blow up phenomenon for the integrable Novikov equation. J Math Anal Appl. 2012;385:551–558.
   Web of Science ®Google Scholar
• Ni L , Zhou Y . Well-posedness and persistence properties for the Novikov equation. J Differ Equ. 2011;250:3002–3021.
   Web of Science ®Google Scholar
• Yan W , Li Y , Zhang Y . The Cauchy problem for the integrable Novikov equation. J Differ Equ. 2012;253:298–318.
   Web of Science ®Google Scholar
• Yan W , Li Y , Zhang Y . Global existence and blow-up phenomena for the weakly dissipative Novikov equation. Nonlinear Anal. 2012;75:2464–2473.
   Web of Science ®Google Scholar
• Costantin A , Lannes D . The hydrodynamical of relevance of Camassa--Holm and Degasperis-Procesi equations. Arch Ration Mech Anal. 2009;192:165–186.
   Web of Science ®Google Scholar
• Camassa R , Holm DD . An integrable shallow water equation with peaked solitons. Phys Rev Lett. 1993;71:1661–1664.
   PubMed Web of Science ®Google Scholar
• Fokas A , Fuchssteiner BS . Symplectic structures, their Bäcklund transformation and hereditary symmetries. Phys D. 1981;4:47–66.
   Web of Science ®Google Scholar
• Boutet de Monvel A , Kostenko A , Shepelsky D , et al . Long-time asymptotics for the Camassa--Holm equation. SIAM J Math Anal. 2009;41:1559–1588.
   Web of Science ®Google Scholar
• Constantin A . On the inverse spectral problem for the Camassa--Holm equation. J Funct Anal. 1998;155:352–363.
   Web of Science ®Google Scholar
• Constantin A . On the scattering problem for the Camassa--Holm equation. Proc Roy Soc London A. 2001;457:953–970.
   Web of Science ®Google Scholar
• Constantin A , Gerdjikov VS , Ivanov RI . Inverse scattering transform for the Camassa--Holm equation. Inverse Probl. 2006;22:2197–2207.
   Web of Science ®Google Scholar
• Constantin A , McKean HP . A shallow water equation on the circle. Commun Pure Appl Math. 1999;52:949–982.
   Web of Science ®Google Scholar
• Eckhardt J . The inverse spectral transform for the conservative Camassa--Holm flow with decaying initial data. Arch Ration Mech Anal. 2017;224:21–52.
   Web of Science ®Google Scholar
• Camassa R , Holm DD , Hyman JM . A new integrable shallow water equation. Adv Appl Mech. 1994;31:1–33.
   Google Scholar
• Constantin A , Escher J . Wave breaking for nonlinear nonlocal shallow water equations. Acta Math. 1998;181:229–243.
   Web of Science ®Google Scholar
• Constantin A . The trajectories of particles in Stokes waves. Invent Math. 2006;166:523–535.
   Web of Science ®Google Scholar
• Constantin A . Particle trajectories in extreme Stokes waves. IMA J Appl Math. 2012;77:293–307.
   Web of Science ®Google Scholar
• Constantin A , Escher J . Analyticity of periodic traveling free surface water waves with vorticity. Ann Math. 2011;173:559–568.
   Web of Science ®Google Scholar
• Toland JF . Stokes waves. Topol Methods Nonlinear Anal. 1996;7:1–48.
   Google Scholar
• Constantin A , Strauss WA . Stability of peakons. Commun Pure Appl Math. 2000;53:603–610.
   Web of Science ®Google Scholar
• Constantin A , Strauss WA . Stability of the Camassa--Holm solitons. J Nonlinear Sci. 2002;12:415–422.
   Web of Science ®Google Scholar
• Rodríguez-Blanco G . On the Cauchy problem for the Camassa--Holm equation. Nonlinear Anal. 2001;46:309–327.
   Web of Science ®Google Scholar
• Constantin A , Escher J . Well-posedness, global existence, and blow up phenomena for a periodic quasi-linear hyperbolic equation. Commun Pure Appl Math. 1998;51:475–504.
   Web of Science ®Google Scholar
• Costantin A , Escher J . Global existence of solutions and breaking waves for a shallow water equation. Ann Sc Norm Super Pisa CL Sci. 1998;26:303–328.
   Google Scholar
• Danchin R . A few remarks on the Camassa--Holm equation. Differ Integral Equ. 2001;14:953–988.
   Google Scholar
• Constantin A , Molinet L . Global weak solutions for a shallow water equation. Commun Math Phys. 2000;211:45–61.
   Web of Science ®Google Scholar
• Xin Z , Zhang P . On the weak solutions to a shallow water equation. Commun Pure Appl Math. 2000;53:1411–1433.
   Web of Science ®Google Scholar
• Constantin A . Finite propagation speed for the Camassa--Holm equation. J Math Phys. 2005;46(2):023506. 4 p.
   Web of Science ®Google Scholar
• Henry D . Compactly supported solutions of the Camassa--Holm equation. J Nonlinear Math Phys. 2005;12:342–347.
   Web of Science ®Google Scholar
• Lenells J . Infinite propagation speed of the Camassa--Holm equation. J Math Anal Appl. 2007;325:1468–1478.
   Web of Science ®Google Scholar
• Brandolese L . Breakdown for the Camassa--Holm equation using decay criteria and persistence in weighted spaces. Int Math Res Not IMRN. 2012;22:5161–5181.
   Google Scholar
• Himonas A , Misiolek G , Ponce G , et al . Persistence properties and unique continuation of solutions of the Camassa--Holm equation. Commun Math Phys. 2007;271:511–522.
   Web of Science ®Google Scholar
• Constantin A , Ivanov R . On an integrable two-component Camassa--Holm shallow water system. Phys Lett A. 2008;372:7129–7132.
   Web of Science ®Google Scholar
• Escher J , Lechtenfeld O , Yin Z . Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation. Discrete Contin Dyn Syst Ser A. 2007;19:493–513.
   Web of Science ®Google Scholar
• Gui G , Liu Y . On the global existence and wave-breaking criteria for the two-component Camassa-Holm system. J Funct Anal. 2010;258:4251–4278.
   Web of Science ®Google Scholar
• Guan C , Yin Z . Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system. J Differ Equ. 2010;248:2003–2014.
   Web of Science ®Google Scholar
• Guan C , Yin Z . Global weak solutions for a two-component Camassa--Holm shallow water system. J Funct Anal. 2011;260:1132–1154.
   Web of Science ®Google Scholar
• Guan C , He H , Yin Z . Well-posedness, blow-up phenomena and persistence properties for a two-component water wave system. Nonlinear Anal Real World Appl. 2015;25:219–237.
   Web of Science ®Google Scholar
• Fonseca G , Ponce G . The IVP for the Benjamin-one equation in weighted Sobolev spaces. J Funct Anal. 2011;260:436–459.
   Web of Science ®Google Scholar
• Kohlmann M . The two-component Camassa--Holm system in weighted Lp spaces. ZAMM Z Angew Math Mech. 2014;94:264–272.
   Web of Science ®Google Scholar
• Aldroubi A , Gröchenig K . Nonuniform sampling and reconstruction in shift-invariant spaces. SIAM Rev. 2001;43:585–620.
   Web of Science ®Google Scholar
• Gröchenig K . Weight functions in time-frequency analysis. In: Pseudo-differential operators: partial differential equations and time-frequency analysis. Vol. 52, Fields Institute Communications. Providence (RI): American Mathematical Society; 2007. p. 343–366.
   Google Scholar
• Luo W , Yin Z . Well-posedness and persistence property for four-component Novikov system with peakon solutions. Monatsh Math. 2015;180:1–39.
   Web of Science ®Google Scholar
• Zhou S , Mu C . The properties of solutions for a generalized b-family equation with peakons. J Nonlinear Sci. 2013;23:863–889.
   Web of Science ®Google Scholar