Global existence for two extended Navier-Stokes systems

Mihaela Ignatova, Gautam Iyer, James P. Kelliher, Robert L. Pego, Arghir D. Zarnescu

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We prove global existence of weak solutions to two systems of equations which extend the dynamics of the Navier-Stokes equations for incompressible viscous flow with no-slip boundary condition. The systems of equations we consider arise as formal limits of time discrete pressure-Poisson schemes introduced by Johnston & Liu [J. Comput. Phys. 199, 221-259, 2004] and by Shirokoff & Rosales [J. Comput. Phys. 230, 8619-8646, 2011] when the initial data does not satisfy the required compatibility condition. Unlike the results of Iyer et al. [J. Math. Phys. 53, 115605, 2012], our approach proves existence of weak solutions in domains with less than C1 regularity. Our approach also addresses uniqueness in 2D and higher regularity.

Original languageEnglish (US)
Pages (from-to)249-267
Number of pages19
JournalCommunications in Mathematical Sciences
Issue number1
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


  • Global well-posedness
  • Navier-stokes
  • Numerics

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    Ignatova, M., Iyer, G., Kelliher, J. P., Pego, R. L., & Zarnescu, A. D. (2014). Global existence for two extended Navier-Stokes systems. Communications in Mathematical Sciences, 13(1), 249-267.