Blow-up analysis for a periodic two-component μ-Hunter–Saxton system
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Zuo, D.: A two-component μ-Hunter–Saxton equation. Inverse Probl. 26, 085003 (2010)
Liu, J., Yin, Z.: On the Cauchy problem of a periodic 2-component μ-Hunter–Saxton system. Nonlinear Anal. 75(1), 131–142 (2012)
Liu, J., Yin, Z.: Global weak solutions for a periodic two-component μ-Hunter–Saxton system. Monatshefte Math. 168, 503–521 (2012)
Khesin, B., Lenells, J., Misiolek, G.: Generalized Hunter–Saxton equation and the geometry of the group of circle diffeomorphisms. Math. Ann. 342, 617–656 (2008)
Lenells, J., Misiolek, G., Tiǧlay, F.: Integrable evolution equations on space of tensor densities and their peakon solutions. Commun. Math. Phys. 299, 129–161 (2010)
Fu, Y., Liu, Y., Qu, C.: On the blow-up structure for the generalized periodic Camassa–Holm and Degasperis–Procesi equations. J. Funct. Anal. 262, 3125–3158 (2012)
Lv, G., Wang, X.: Holder continuity on μ–b equation. Nonlinear Anal. 102, 30–35 (2014)
Escher, J.: Non-metric two-component Euler equation on the circle. Monatshefte Math. 167, 449–459 (2012)
Moon, B., Liu, Y.: Wave breaking and global existence for the generalized periodic two-component Hunter–Saxton system. J. Differ. Equ. 253, 319–355 (2012)
Wunsch, M.: On the Hunter–Saxton system. Discrete Contin. Dyn. Syst. 12, 647–656 (2009)
Wunsch, M.: Weak geodesic flow on a semi-direct product and global solutions to the periodic Hunter–Saxton system. Nonlinear Anal. 74, 4951–4960 (2011)
Moon, B.: Solitary wave solutions of the generalized two-component Hunter–Saxton system. Nonlinear Anal., Theory Methods Appl. 89, 242–249 (2013)
Guo, F., Gao, H.J., Liu, Y.: On the wave-breaking phenomena for the two-component Dullin–Gottwald–Holm system. J. Lond. Math. Soc. 86, 810–834 (2012)
Zhu, M., Xu, J.X.: On the wave-breaking phenomena for the periodic two-component Dullin–Gottwald–Holm system. J. Math. Anal. Appl. 391, 415–428 (2012)
Constantin, A., Ivanov, R.I.: On an integrable two-component Camassa–Holm shallow water system. Phys. Lett. A 372, 7129–7132 (2008)
Escher, J., Lechtenfeld, O., Yin, Z.: Well-posedness and blow-up phenomena for the 2-component Camassa–Holm equation. Discrete Contin. Dyn. Syst. 19, 493–513 (2007)
Gui, G., Liu, Y.: On the Cauchy problem for the two-component Camassa–Holm system. Math. Z. 268(1–2), 45–66 (2011)
Gui, G., Liu, Y.: On the global existence and wave-breaking criteria for the two-component Camassa–Holm system. J. Funct. Anal. 258, 4251–4278 (2010)
Guo, Z., Zhou, Y.: On solutions to a two-component generalized Camassa–Holm equation. Stud. Appl. Math. 124, 307–322 (2010)
Chen, R.M., Liu, Y.: Wave breaking and global existence for a generalized two-component Camassa–Holm system. Int. Math. Res. Not. 6, 1381–1416 (2011)
Ivanov, R.: Two-component integrable systems modelling shallow water waves: the constant vorticity case. Wave Motion 46, 389–396 (2009)
Zhang, P.Z., Liu, Y.: Stability of solitary waves and wave-breaking phenomena for the two-component Camassa–Holm system. Int. Math. Res. Not. 211, 1981–2021 (2010)
Lv, G., Wang, X.: Non-uniform dependence on initial data of a modified periodic two-component Camassa–Holm system. Z. Angew. Math. Mech. 95, 444–456 (2015)
Lv, G., Wang, X.: On the Cauchy problem for a two-component b-family system. Nonlinear Anal. 111, 1–14 (2014)
Kato, T.: Quasi-linear equations of evolution with applications to partial differential equations. In: Spectral Theory and Differential Equations. Lecture Notes in Math., vol. 448, pp. 25–70. Springer, Berlin (1975)
Constantin, A., Escher, J.: Wave-breaking for nonlinear nonlocal shallow water equations. Acta Math. 181, 229–243 (1998)