The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system
MetadataShow full item record
The blow-up solutions of the Cauchy problem for the Davey–Stewartson system, which is a model equation in the theory of shallow water waves, are investigated. Firstly, the existence of the ground state for the system derives the best constant of a Gagliardo–Nirenberg type inequality and the variational character of the ground state. Secondly, the blow-up threshold of the Davey–Stewartson system is developed in R3. Thirdly, the mass concentration is established for all the blow-up solutions of the system in R2. Finally, the existence of the minimal blow-up solutions in R2 is constructed by using the pseudo-conformal invariance. The profile of the minimal blow-up solutions as t --> T (blow-up time) is in detail investigated in terms of the ground state.
Showing items related by title, author, creator and subject.
Li, X.; Zhang, J.; Lai, S.; Wu, Yong Hong (2012)The blow-up solutions of the Cauchy problem for a generalized Davey–Stewartson system, which models the wave propagation in a bulk medium made of an elastic material with coupled stresses, are investigated. The mass ...
Lin, Qun (2009)We develop well-posedness theory and analytical and numerical solution techniques for Boussinesq-type equations. Firstly, we consider the Cauchy problem for a generalized Boussinesq equation. We show that under suitable ...
Ming, Sen; Yang, Han; Wu, Yong Hong (2014)The weakly dissipative 2-component Camassa-Holm system is considered. A local well-posedness for the system in Besov spaces is established by using the Littlewood-Paley theory and a priori estimates for the solutions of ...