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.

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 {<i>\ensuremath{\mu}</i>-Hunter{\textendash}Saxton} equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {267--279}, publisher = {Elsevier}, volume = {31}, number = {2}, year = {2014}, doi = {10.1016/j.anihpc.2013.02.008}, zbl = {1302.35320}, mrnumber = {3181669}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.02.008/} }

TY - JOUR AU - Liu, Jingjing AU - Yin, Zhaoyang TI - On the Cauchy problem of a weakly dissipative <i>μ</i>-Hunter–Saxton equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 DA - 2014/// SP - 267 EP - 279 VL - 31 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.02.008/ UR - https://zbmath.org/?q=an%3A1302.35320 UR - https://www.ams.org/mathscinet-getitem?mr=3181669 UR - https://doi.org/10.1016/j.anihpc.2013.02.008 DO - 10.1016/j.anihpc.2013.02.008 LA - en ID - AIHPC_2014__31_2_267_0 ER -

%0 Journal Article %A Liu, Jingjing %A Yin, Zhaoyang %T On the Cauchy problem of a weakly dissipative <i>μ</i>-Hunter–Saxton equation %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 267-279 %V 31 %N 2 %I Elsevier %U https://doi.org/10.1016/j.anihpc.2013.02.008 %R 10.1016/j.anihpc.2013.02.008 %G en %F AIHPC_2014__31_2_267_0

Liu, Jingjing; Yin, Zhaoyang. On the Cauchy problem of a weakly dissipativeμ-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/articles/10.1016/j.anihpc.2013.02.008/

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