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J. E. Marsden, L. Sirovich and F. John, “Infinite-Dimensional Dynamical Systems in Mechanics and Physics,” Applied Mathematical Sciences, Vol. 68, 1997, Springer Verlag, New York, pp. 15-25.

has been cited by the following article:

• TITLE: On the Incompressible Navier-Stokes Equations with Damping

  AUTHORS: Wenyan Zhao, Zhibo Zheng

  KEYWORDS: Incompressible Navier-Stokes Equation; Solution; Maximal Attractor; Limit-Behavior

  JOURNAL NAME: Applied Mathematics, Vol.4 No.4, April 26, 2013

  ABSTRACT: We consider dynamics system with damping, which are obtained by some transformations from the system of incompressible Navier-Stokes equations. These have similar properties to original Navier-Stokes equations the scaling invariance. Due to the presence of the damping term, conclusions are different with proving the origin of the incompressible Navier-Stokes equations and get some new conclusions. For one form of dynamics system with damping we prove the existence of solution, and get the existence of the attractors. Moreover, we discuss with limit-behavior the deformations of the Navier-Stokes equation.