Abstract
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 language | English (US) |
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Pages (from-to) | 249-267 |
Number of pages | 19 |
Journal | Communications in Mathematical Sciences |
Volume | 13 |
Issue number | 1 |
DOIs | |
State | Published - 2014 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics
Keywords
- Global well-posedness
- Navier-stokes
- Numerics