Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899433 | Journal of Mathematical Analysis and Applications | 2018 | 35 Pages |
Abstract
In this paper, we consider the Cauchy problem for a family of nonlocal complex Ginzburg-Landau equationeâiθut=Îu+(1|x|nâαâ|u|p)|u|pâ2uâλu on Rn, where âÏ/2<θ<Ï/2 and λâR. First, the local well-posedness in Lebesgue spaces is established by a fixed point argument. Then we set up the H2 regularity and derive the energy identities. By constructing some invariant sets, we further find some sufficient conditions on finite time blow-up and global existence for solutions which in particular determines a sharp threshold of initial date when λ>0. In addition, we estimate the lifespan of solutions as a function of θ and obtain the lower bound of the maximal existence time for λâR.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xiaoliang Li, Baiyu Liu,