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Volume 32, Issue 1
Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain

Xin-Guang Yang & Shubin Wang

DOI: 10.4208/jpde.v32.n1.6

J. Part. Diff. Eq., 32 (2019), pp. 77-92.

Published online: 2019-04

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  • Abstract

This paper is concerned with the global well-posedness and regularity of weak solutions for the 2D non-autonomous incompressible Navier-Stokes equation with a inhomogeneous boundary condition in Lipschitz-like domain. Using the estimate for governing steady state equation and Hardy’s inequality, the existence and regularity of global unique weak solution can be proved. Moreover, these results also hold for 2D Navier-Stokes equation with Rayleigh’s friction and Navier-Stokes-Voigt flow, but invalid for three dimension.

  • Keywords

Non-autonomous Navier-Stokes equation Lipshitz-like domain background flow function.

  • AMS Subject Headings

35B40, 35B41, 35Q30, 76D03, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yangxinguang@hotmail.com (Xin-Guang Yang)

wangshubin@zzu.edu.cn (Shubin Wang)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-32-77, author = {Yang , Xin-Guang and Wang , Shubin}, title = {Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {32}, number = {1}, pages = {77--92}, abstract = {

This paper is concerned with the global well-posedness and regularity of weak solutions for the 2D non-autonomous incompressible Navier-Stokes equation with a inhomogeneous boundary condition in Lipschitz-like domain. Using the estimate for governing steady state equation and Hardy’s inequality, the existence and regularity of global unique weak solution can be proved. Moreover, these results also hold for 2D Navier-Stokes equation with Rayleigh’s friction and Navier-Stokes-Voigt flow, but invalid for three dimension.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v32.n1.6}, url = {http://global-sci.org/intro/article_detail/jpde/13124.html} }
TY - JOUR T1 - Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain AU - Yang , Xin-Guang AU - Wang , Shubin JO - Journal of Partial Differential Equations VL - 1 SP - 77 EP - 92 PY - 2019 DA - 2019/04 SN - 32 DO - http://doi.org/10.4208/jpde.v32.n1.6 UR - https://global-sci.org/intro/article_detail/jpde/13124.html KW - Non-autonomous Navier-Stokes equation KW - Lipshitz-like domain KW - background flow function. AB -

This paper is concerned with the global well-posedness and regularity of weak solutions for the 2D non-autonomous incompressible Navier-Stokes equation with a inhomogeneous boundary condition in Lipschitz-like domain. Using the estimate for governing steady state equation and Hardy’s inequality, the existence and regularity of global unique weak solution can be proved. Moreover, these results also hold for 2D Navier-Stokes equation with Rayleigh’s friction and Navier-Stokes-Voigt flow, but invalid for three dimension.

Xin-Guang Yang & Shubin Wang. (2019). Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain. Journal of Partial Differential Equations. 32 (1). 77-92. doi:10.4208/jpde.v32.n1.6
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