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Research on dynamic behavior of generalized DS system

Author: LuJing
Tutor: MiaoChangXing
School: Chinese Academy of Engineering Physics
Course: Basic mathematics
Keywords: Davey-Stewartson system scatter global well-posedness blow up concentration-compactness
CLC: O175
Type: Master's thesis
Year: 2013
Downloads: 7
Quote: 0
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Abstract


In this paper, we consider the Cauchy problem for the generalized Davey-Stewartson system where a>0,b1b2>0,4/3+1<p<5. By introducing an operator E1f(ξ)=(?)(ξ), the above system can be reduced to the following Cauchy problemWe first use a variational approach to give a dichotomy of blow-up and scattering for the solution of mass supercritical equation with the initial data satisfying J(u0)<J(R), where J stands for the Lagrange functional. By establishing the localized Virial identity, we obtain that when Q(u0)<0, then the solution u blows up both forward and backward in time. The basic strategy to establish the scattering theory is the concentration-compactness arguments from Kenig and Merle [20]. Specifically, suppose that when J(u0)<J(R),Q(u0)>0, the solution u does not scatter. Then by concentration-compactness argument and the blow up result, we will extract the unique bubble and obtain the critical solution. Hence the compactness of the critical element and the localized Virial identity lead to a contrcdiction.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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