On global well-posedness to 3D Navier-Stokes-Landau-Lifshitz equations

Ning Duan; Xiaopeng Zhao; Ning Duan; Xiaopeng Zhao

doi:10.3934/math.2020416

AIMS Mathematics

2020, Volume 5, Issue 6: 6457-6463. doi: 10.3934/math.2020416

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Research article

On global well-posedness to 3D Navier-Stokes-Landau-Lifshitz equations

Ning Duan ,
Xiaopeng Zhao ^,

College of Sciences, Northeastern University, Shenyang 110819, P. R. China

Received: 09 July 2020 Accepted: 13 August 2020 Published: 19 August 2020
MSC : 35Q35, 35D35, 76D05

In this paper, we prove the global well-posedness of solutions for the Cauchy problem of three-dimensional incompressible Navier-Stokes-Landau-Lifshitz equations under the condition that $\|u_0\|_{H^{\frac12}}+\|\nabla d_0\|_{H^{\frac12+\varepsilon}}$ ($\varepsilon>0)$ is sufficiently small. This result can be seen as an improvement of the previous paper ^[20].
- Navier-Stokes-Landau-Lifshitz equations,
- local existence,
- global well-posedness
Citation: Ning Duan, Xiaopeng Zhao. On global well-posedness to 3D Navier-Stokes-Landau-Lifshitz equations[J]. AIMS Mathematics, 2020, 5(6): 6457-6463. doi: 10.3934/math.2020416

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Abstract

In this paper, we prove the global well-posedness of solutions for the Cauchy problem of three-dimensional incompressible Navier-Stokes-Landau-Lifshitz equations under the condition that $\|u_0\|_{H^{\frac12}}+\|\nabla d_0\|_{H^{\frac12+\varepsilon}}$ ($\varepsilon>0)$ is sufficiently small. This result can be seen as an improvement of the previous paper ^[20].

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