On continuation properties after blow-up time for -critical gKdV equations

  • Yang Lan

    Universität Basel, Switzerland
On continuation properties after blow-up time for $L^2$-critical gKdV equations cover

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Abstract

In this paper, we consider a blow-up solution (close to the soliton manifold) to the -critical gKdV equation , with finite blow-up time . We expect to construct a natural extension of after the blow-up time. To do this, we consider the solution to the saturated -critical gKdV equation with the same initial data, where and . A standard argument shows that is always global in time. Moreover, for all , converges to in as . We prove in this paper that for all , as , in a certain sense. This limiting function is a weak solution to the unperturbed -critical gKdV equations, hence can be viewed as a natural extension of after the blow-up time.

Cite this article

Yang Lan, On continuation properties after blow-up time for -critical gKdV equations. Rev. Mat. Iberoam. 36 (2020), no. 4, pp. 957–984

DOI 10.4171/RMI/1154