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

  • 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.

    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

    Related Papers:

  • 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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