On the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 2, p. 267-279
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In this paper, we study the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation. We first establish the local well-posedness for the weakly dissipative μ-Hunter–Saxton equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation.
DOI : https://doi.org/10.1016/j.anihpc.2013.02.008
Classification:  35Q35,  35G25,  58D05
Keywords: A weakly dissipative μ-Hunter–Saxton, Blow-up scenario, Blow-up, Strong solutions, Global existence
@article{AIHPC_2014__31_2_267_0,
     author = {Liu, Jingjing and Yin, Zhaoyang},
     title = {On the Cauchy problem of a weakly dissipative $\mu$-Hunter--Saxton equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {31},
     number = {2},
     year = {2014},
     pages = {267-279},
     doi = {10.1016/j.anihpc.2013.02.008},
     zbl = {1302.35320},
     mrnumber = {3181669},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2014__31_2_267_0}
}
Liu, Jingjing; Yin, Zhaoyang. On the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 2, pp. 267-279. doi : 10.1016/j.anihpc.2013.02.008. http://www.numdam.org/item/AIHPC_2014__31_2_267_0/

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