References
- Hakkaev S, Kirchev K. Local well-posedness and orbital stability of solitary wave solutions for the generalized Camassa-Holm equation. Comm. Part. Diff. Eq. 2005;30:761–781.
- Bona J, Smith R. The initial-value problem for the Korteweg-de Vries equation. Phil. Trans. Roy. Soc. London Ser. A. 1975;278:555–601.
- Grillakis M, Shatah J, Strauss W. Stability theory of solitary waves in the presence of symmetry. J. Funct. Anal. 1987;74:160–197.
- Camassa R, Holm D. An integrable shallow wateer equation with peaked solitons. Phys. Rev. Lett. 1993;71:1661–1664.
- Fokas A, Fuchssteiner B. Symplectic structures, their Bäklund transformations and hereditray symmetries. Phys. D. 1981;4:47–66.
- Misiolek G. A shallow water equation as a geodesic flow on the Bott-Virasoro group. J. Geom. Phys. 1998;24:203–208.
- Constantin A. On the Cauchy problem for the periodic Camassa-Holm equation. J. Diff. Eqns. 1997;10:218–235.
- Constantin A. Existence of permanent and breaking waves for a shallow water equation: A geometric approach. Ann. Inst. Fourier (Grenoble). 2000;50:321–362.
- Constantin A, Escher J. Wave breaking for nonlinear nonlocal shallow water equations. Acta Math. 1998;181:229–243.
- Constantin A, Escher J. Well-posedness, global existence and blow-up phenomena for a periodic quasi-linear hyperbolic equation. Comm. Pure Appl. Math. 1998;51:475–504.
- Mckean H. Breakdown of a shallow water equation. Asian J. Math. 1998;2(4):867–874.
- Xin Z, Zhang P. On the weak solutions to a shallow water equation. Commu. Pure Appl. Math. 2000;53:1411–1433.
- Kato T. Quasi-linear equations of evolution, with applications to partial differential equations. Vol, 448, In: Spectral theory and differential equations. Lecture notes in Math. Berlin: Spring Verlag; 1975. p. 25–70.
- Blanco G. On the Cauchy problem for the Camassa-Holm equation. Nonlinear Anal. TMA. 2001;46:309–327.
- Constantin A, Strauss W. Stability of solitons. Comm. Pure Appl. Math. 2000;53:603–610.
- Constantin A, Strauss W. Stability of the Camassa-Holm solitons. J. Nonlinear Sci. 2002;12: 415–422.
- Constantin A, Molinet L. Global weak solutions for a shallow water equation. Comm. Math. Phys. 1998;211:45–61.
- Li Y, Olver P. Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. J. Diff. Eqns. 2000;162:27–63.
- Constantin A, Mckean H. A shallow water equation on the circle. Comm. Pure Appl. Math. 1999;52:949–982.
- Danchin R. A few remarks on the Camassa-Holm equation. Diff. Int. Eqns. 2001;14:953–988.
- Danchin R. Fourier analysis method for PDEs, Lecture, Notes. 14 November, 2005.
- Danchin R. A note on well-posedness for Camassa-Holm equation. J. Diff. Eqns. 2003;192: 429–444.
- Constantin A, Lannes D. The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations. Arch. Ration. Mech. Anal. 2007;192:165–186.
- Lenells J. Stability of periodic peakons. Internat. Math. Res. Notices. 2004;10:485–499.
- Lenells J. The correspondence between KdV and Camassa-Holm. Internat. Math. Res. Notices. 2004;71:3797–3811.
- Lenells J. Travelling wave equations of the Camassa-Holm equation. J. Diff. Eqns. 2005;217:393–430.
- Bressan A, Constantin A. Global conservative solutions of the Camassa-Holm equation. Arch. Ration. Mech. Anal. 2007;183:215–239.
- Bressan A, Constantin A. Global dissipative solutions of the Camassa-Holm equation. Appl. Anal. 2007;5:1–27.
- Yin Z. On the Cauchy problem for the generalized Camassa-Holm equation. Nonlinear Anal. TMA. 2007;66:460–471.
- Wu S, Yin Z. Global existence and blow-up phenomena for the weakly dissipative Camassa-Holm equation. J. Diff. Eqns. 2009;246:4309–4321.
- Vishik M. Hydrodynamics in Besov spaces. Arch. Ration. Mech. Anal. 1998;145:197–214.
- Danchin R, Fanelli F. The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces. J. Math. Pures Appl. 2011;96:253–278.
- Danchin R, Mucha P. A critical functional framework for the inhomogeneous Navier-Stokes equations in the half-space. J. Funct. Anal. 2009;256:881–927.
- Danchin R. On the well-posedness of the incompressible density-dependent Euler equations in the Lp framework. J. Diff. Eqns. 2010;248:2130–2170.
- Gui G, Liu Y. On the Cauchy problem for the two-compenent Camassa-Holm system. Math. Z. 2011;268:45–66.
- Yan K, Yin Z. On the Cauchy problem for a two-compnent Degasperis-Procesi system. J. Diff. Eqns. 2012;252:2131–2159.
- Ni L, Zhou Y. Well-posedness and persistence properties for the Novikov equation. J. Diff. Eqns. 2011;250:3002–3021.
- Chemin JY. Localization in Fourier space and Navier-Stokes in phase space analysis of partial differential equations. In: CRM Series Scuola Norm. Pisa: Sup; 2004. p, 53–136.
- Gui G, Liu Y, Olver P, Qu C. Wave-breaking and peakon for a modified Camassa-Holm equation. Commu. Math. Phys, 2013; 319:731–759
- Bahouri H, Chemin J, Danchin R. Fourier analysis and nonlinear partial differential equations. Berlin: Springer-Verlag; 2011.