Local well-posedness of perturbed Navier-Stokes system around Landau solutions

Jingjing Zhang; Ting Zhang; Jingjing Zhang; Ting Zhang

doi:10.3934/era.2021010

Electronic Research Archive

2021, Volume 29, Issue 4: 2719-2739. doi: 10.3934/era.2021010

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Local well-posedness of perturbed Navier-Stokes system around Landau solutions

Jingjing Zhang ,
Ting Zhang ^,

School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

Received: 01 December 2020 Published: 22 February 2021
Primary: 35Q30; Secondary: 49K40

For the incompressible Navier-Stokes system, when initial data are uniformly locally square integral, the local existence of solutions has been obtained. In this paper, we consider perturbed system and show that perturbed solutions of Landau solutions to the Navier-Stokes system exist locally under $ L^q_{\text{uloc}} $-perturbations, $ q\geq 2 $. Furthermore, when $ q\geq 3, $ the solution is well-posed. Precisely, we give the explicit formula of the pressure term.
- Local well-posedness,
- Navier-Stokes system,
- Landau solutions
Citation: Jingjing Zhang, Ting Zhang. Local well-posedness of perturbed Navier-Stokes system around Landau solutions[J]. Electronic Research Archive, 2021, 29(4): 2719-2739. doi: 10.3934/era.2021010

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Abstract

For the incompressible Navier-Stokes system, when initial data are uniformly locally square integral, the local existence of solutions has been obtained. In this paper, we consider perturbed system and show that perturbed solutions of Landau solutions to the Navier-Stokes system exist locally under $ L^q_{\text{uloc}} $-perturbations, $ q\geq 2 $. Furthermore, when $ q\geq 3, $ the solution is well-posed. Precisely, we give the explicit formula of the pressure term.

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