Date | Sep 11, 2018 |
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Speaker | 조용근 |

Dept. | 전북대학교 |

Room | 27-116 |

Time | 16:30-18:00 |

In this talk we consider inhomogeneous cubic-quintic NLS in space dimension $d=3$
:

$$rm(ICQNLS)quadi{u}_{t}=-Deltau+{K}_{1}(x)|u{|}^{2}u+{K}_{2}(x)|u{|}^{4}u.$$

We discuss local well-posedness, finite time blowup, and small data scattering and non-scattering for the ICQNLS when ${K}_{1},{K}_{2}inC(mathbb{R}^{3})cap{C}^{4}(mathbb{R}^{3}setminus0)$ satisfy growth condition $|partia{l}^{j}{K}_{i}(x)|lesssim|x{|}^{{b}_{i}-j}(j=0,1,2,3)$ for some ${b}_{i}>0$ and for $xneq0$ . To this end we use the Sobolev inequality for the functions $fin{H}^{1}$ such that $|mathbfLf{|}_{{H}^{1}}<infty$ , where $mathbfL$ is the angular momentum operator defined by $mathbfL=xtimes(-inabla)$ .

We discuss local well-posedness, finite time blowup, and small data scattering and non-scattering for the ICQNLS when ${K}_{1},{K}_{2}inC(mathbb{R}^{3})cap{C}^{4}(mathbb{R}^{3}setminus0)$ satisfy growth condition $|partia{l}^{j}{K}_{i}(x)|lesssim|x{|}^{{b}_{i}-j}(j=0,1,2,3)$ for some ${b}_{i}>0$ and for $xneq0$ . To this end we use the Sobolev inequality for the functions $fin{H}^{1}$ such that $|mathbfLf{|}_{{H}^{1}}<infty$ , where $mathbfL$ is the angular momentum operator defined by $mathbfL=xtimes(-inabla)$ .

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