Local Existence of Solution to the Incompressible Oldroyd Model Equations

LIU Yun, YUAN Bao-quan

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

Chinese Quarterly Journal of Mathematics >

2017 , Vol. 32 >Issue 4: 331 - 344

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.04.001

Local Existence of Solution to the Incompressible Oldroyd Model Equations

Expand

School of Mathematics and Information Science, Henan Polytechnic University

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.

Received date: 2017-02-03

Online published: 2020-10-20

Supported by

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

Fold

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

Cite this article

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

Options

Outlines

模态框（Modal）标题

School of Mathematics and Information Science, Henan Polytechnic University

Abstract

Cite this article