Global weak solutions and smooth solutions for a two-component Hunter-Saxton system. (English) Zbl 1272.76029
Summary: In this paper, we mainly study the initial value problem of a two-component Hunter-Saxton system. By the method of characteristics, we first show that the system has global smooth solutions and blowing up smooth solutions. By using the obtained a priori estimates on smooth solutions, we then prove the existence of global weak solutions to the system.{
©2011 American Institute of Physics}
©2011 American Institute of Physics}
MSC:
| 76A15 | Liquid crystals |
| 35Q35 | PDEs in connection with fluid mechanics |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35B44 | Blow-up in context of PDEs |
| 35D30 | Weak solutions to PDEs |
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