Estimates on fractional power dissipative equations in function spaces |
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Authors: | Jiecheng Chen Qingquan Deng Yong Ding Dashan Fan |
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Affiliation: | a Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Chinab Department of Mathematics, Zhejiang University, Hangzhou 310027, Chinac School of Mathematical Sciences, Beijing Normal University, Beijing 100875, Chinad School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems (BNU), Ministry of Education, Beijing Normal University, Beijing 100875, Chinae Department of Mathematics, University of Wisconsin—Milwaukee, Milwaukee, WI 53201, USA |
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Abstract: | We study the fractional power dissipative equations, whose fundamental semigroup is given by e−t(−Δ)α with α>0. By using an argument of duality and interpolation, we extend space-time estimates of the fractional power dissipative equations in Lebesgue spaces to the Hardy spaces and the modulation spaces. These results are substantial extensions of some known results. As applications, we study both local and global well-posedness of the Cauchy problem for the nonlinear fractional power dissipative equation ut+(−Δ)αu=|u|mu for initial data in the modulation spaces. |
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Keywords: | 42B30 42B25 42B35 35J15 |
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