不可压缩Oldroyd方程局部解的存在性

doi:10.13371/j.cnki.chin.q.j.m.2017.04.001

数学季刊 ›› 2017, Vol. 32 ›› Issue (4): 331-344.doi: 10.13371/j.cnki.chin.q.j.m.2017.04.001

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不可压缩Oldroyd方程局部解的存在性

School of Mathematics and Information Science, Henan Polytechnic University

收稿日期:2017-02-03 出版日期:2017-12-30 发布日期:2020-10-20
作者简介: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.
基金资助:
Supported by the National Natural Science Foundation of China(11471103)；

Local Existence of Solution to the Incompressible Oldroyd Model Equations

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.
Supported by:
Supported by the National Natural Science Foundation of China(11471103)；

摘要/Abstract

摘要： This paper investigates the local-in-time existence and uniqueness of strong solutions in H^s for s >n/2 to the incompressible Oldroyd model equations in Rⁿ, n = 2, 3.The result reads: if u₀, F₀∈ H^s（Rⁿ） with s >n/2, then there exists a unique strong solution u, F ∈ C（[0, T]; H^s（Rⁿ））, where T = T（‖u₀‖H^s, ‖F₀‖H^s） is the local existence time.

关键词: Incompressible Oldroyd model, local well-posedness, Friedrichs' method

Abstract: This paper investigates the local-in-time existence and uniqueness of strong solutions in H^s for s >n/2 to the incompressible Oldroyd model equations in Rⁿ, n = 2, 3.The result reads: if u₀, F₀∈ H^s（Rⁿ） with s >n/2, then there exists a unique strong solution u, F ∈ C（[0, T]; H^s（Rⁿ））, where T = T（‖u₀‖H^s, ‖F₀‖H^s） is the local existence time.

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

中图分类号:

刘筠, 原保全.

不可压缩Oldroyd方程局部解的存在性

[J]. 数学季刊, 2017, 32(4): 331-344.

LIU Yun, YUAN Bao-quan. Local Existence of Solution to the Incompressible Oldroyd Model Equations[J]. Chinese Quarterly Journal of Mathematics, 2017, 32(4): 331-344.

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不可压缩Oldroyd方程局部解的存在性

School of Mathematics and Information Science, Henan Polytechnic University

Local Existence of Solution to the Incompressible Oldroyd Model Equations

School of Mathematics and Information Science, Henan Polytechnic University

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