Nonuniform dependence and persistence properties for a two-component Novikov system

References

• Popowicz Z. Double extended cubic peakon equations. Phys Lett A. 2015;379:1240–1245.
   Web of Science ®Google Scholar
• Luo W, Yin Z. Local well-posedness and blow-up criteria for a two-component Novikov system in the critical Besov space. Nonlinear Anal. 2015;122:1–22.
   Web of Science ®Google Scholar
• Novikov V. Generalizations of the Camassa-Holm type equation. J Phys A. 2009;42:342002.
   Google Scholar
• Hone A, Wang J. Integrable peakon equations with cubic nonlinearity. J Phys A. 2008;42:372002.
   Google Scholar
• Constantin A, Escher J. Global existence and blow-up for a shallow water equation. Ann Sc Norm Super Pisa Cl Sci. 1998;26:303–328.
   Google Scholar
• Constantin A, Escher J. Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation. Commun Pure Appl Math. 1998;51:475–504.
   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. Global existence of solutions and breaking waves for a shallow water equation: a geometric approach. Ann Inst Fourier (Grenoble). 2000;50:321–362.
   Web of Science ®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
• 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
• Guan C, Yin Z. Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system. J Diff Eqns. 2010;248:2003–2014.
   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
• Ni L, Zhou Y. Well-posedness and persistence properties for the Novikov equation. J Diff Eqns. 2011;250:3002–3021.
   Web of Science ®Google Scholar
• Tigaly F. The periodic Cauchy problem for Novikov’s equation. Inter Math Res Notices. 2011;20:4633–4648.
   Google Scholar
• Wu X, Yin Z. Well-posedness and global existence for the Novikov equation. Ann Sc Norm Super Pisa Cl Sci. 2012;11(5):707–727.
   Google Scholar
• Wu X, Yin Z. A note on the Cauchy problem of the Novikov equation. Appl Anal. 2013;92:1116–1137.
   Web of Science ®Google Scholar
• Yan W, Li Y, Zhang Y. The Cauchy problem for the integrable Novikov equation. J Diff Eqns. 2012;253:298–318.
   Web of Science ®Google Scholar
• Yan W, Li Y, Zhang Y. The Cauchy problem for the Novikov equation. NoDEA Nonlinear Diff Eqns Appl. 2013;20:1157–1169.
   Web of Science ®Google Scholar
• Lai S, Li N, Wu Y. The existence of global strong and weak solutions for the Novikov equation. J Math Anal Appl. 2013;399:682–691.
   Web of Science ®Google Scholar
• Jiang Z, Ni L. Blow-up phenomenon for the integrable Novikov equation. J Math Anal Appl. 2015;385:551–558.
   Web of Science ®Google Scholar
• Chen G, Chen R, Liu Y. Existence and uniqueness of the global conservative weak solutions for the integrable Novikov equation. 2015. arXiv1509.08569v1.
   Google Scholar
• Lai S. Global weak solutions to the Novikov equation. J Funct Anal. 2013;265:520–544.
   Web of Science ®Google Scholar
• Wu X, Yin Z. Global weak solutions for the Novikov equation. J Phys A. 2011;44:055202.
   Google Scholar
• Liu X, Liu Y, Qu C. Stability of peakons for the Novikov equation. J Math Pures Appl. 2014;101:172–187.
   Web of Science ®Google Scholar
• Himonas A, Kenig C. Non-uniform dependence on initial data for the CH equation on the line. Diff Int Eqns. 2009;22:201–224.
   Web of Science ®Google Scholar
• Himonas A, Kenig C, Misiolek G. Non-uniform dependence for the periodic CH equation. Commun Partial Diff Eqns. 2010;35:1145–1162.
   Web of Science ®Google Scholar
• Holliman C. Non-uniform dependence and well-posedness for the periodic Hunter-Saxton equation. Diff Int Eqns. 2010;23:1159–1194.
   Web of Science ®Google Scholar
• Karapetyan D. Non-uniform dependence and well-posedness for the hyperelastic rod equation. J Diff Eqns. 2010;249:796–826.
   Web of Science ®Google Scholar
• Himonas A, Holliman C. The Cauchy problem for Novikov equation. Nonlinearity. 2012;25:449–479.
   Web of Science ®Google Scholar
• Himonas A, Mantzavinos D. The Cauchy problem for the Fokas-Olver-Rosenau-Qiao equation. Nonlinear Anal. 2014;95:499–529.
   Web of Science ®Google Scholar
• Lv G, Pang P, Wang M. Non-uniform dependence on initial data for the µ-b equation. Z Angew Math Phys. 2013;64:1543–1554.
   Web of Science ®Google Scholar
• Lv G, Wang M. Non-uniform dependence for a modified Camassa-Holm system. J Math Phys. 2012;53:013101.
   Web of Science ®Google Scholar
• Lv G. On the Cauchy problem for a two-component b-family system. Nonlinear Anal. 2014;111:1–14.
   Web of Science ®Google Scholar
• Himonas A, Thompson R. Persistence properties and unique continuation for a generalized Camassa-Holm equation. J Math Phys. 2014;55:091503.
   Web of Science ®Google Scholar
• Kato T. Quasi-linear equations of evolution with applications to partial differential equations. In: Everitt WN, editor. Spectral theory and differential equations. Vol. 448, Lecture notes in mathematics. Berlin: Springer-Verlag; 1975. p. 25–70.
   Google Scholar
• Yan K, Yin Z. Infinite propagation speed and asymptotic behavior for a two-component Degasperis-Procesi system. Monatsh Math. 2016;181(1):217–234.
   Web of Science ®Google Scholar