Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 13-CNA-017 Global existence for two extended Navier-Stokes systems Mihaela IgnatovaDepartment of Mathematics Stanford University Stanford, CA 94305 mihaelai@stanford.edu Gautam IyerDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213gautam@math.cmu.edu James P. KelliherDepartment of Mathematics University of California, Riverside Riverside, California kelliher@math.ucr.edu Robert L. PegoDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213rpego@andrew.cmu.edu Arghir ZarnescuDepartment of Mathematics University of Sussex Pevensey III, Falmer, BN1 9QH, United KingdomA.Zarnescu@sussex.ac.ukAbstract: 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 and Liu (J. Comp. Phys. 199 (2004) 221-259) and by Shirokoff and Rosales (J Comp. Phys 230 (2011) 8619-8646) when the initial data does not satisfy the required compatibility condition. Unlike the results of Iyer et al (J. Math. Phys. 53 (2012) 115605), our approach proves existence of weak solutions in domains with less than $C^1$ regularity. Our approach also addresses uniqueness in 2D and higher regularity. Get the paper in its entirety as  13-CNA-017.pdf