Chinese Quarterly Journal of Mathematics ›› 2017, Vol. 32 ›› Issue (4): 331-344.doi: 10.13371/j.cnki.chin.q.j.m.2017.04.001

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Local Existence of Solution to the Incompressible Oldroyd Model Equations

  

  1. School of Mathematics and Information Science, Henan Polytechnic University

  • Received:2017-02-03 Online:2017-12-30 Published:2020-10-20
  • About author:LIU Yun(1992-), femal, native of Fanxian, Henan, graduate student, engages in partial differential equations and applications; YUAN Bao-quan(1965-), male, native of Jiaozuo, Henan, professor of Henan Polytechnic University, Ph.D., engages in partial di®erential equations and applications. School of Mathematics and Information Science, Henan Polytechnic University, Henan, 454000, China.
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Abstract: This paper investigates the local-in-time existence and uniqueness of strong solutions in Hs for s >n/2 to the incompressible Oldroyd model equations in Rn, n = 2, 3.The result reads: if u0, F0∈ Hs(Rn) with s >n/2, then there exists a unique strong solution u, F ∈ C([0, T]; Hs(Rn)), where T = T(‖u0Hs, ‖F0Hs) is the local existence time. 

Key words: Incompressible Oldroyd model, local well-posedness, Friedrichs' method

CLC Number: