Abstract
In this paper, we consider the Cauchy problem for a nonlinear parabolic system \({u^\epsilon_t - \Delta u^\epsilon + u^\epsilon \cdot \nabla u^\epsilon + \frac{1}{2}u^\epsilon\, {\rm div}\, u^\epsilon - \frac{1}{\epsilon}\nabla\, {\rm div}\, u^\epsilon = 0}\) in \({\mathbb {R}^3 \times (0,\infty)}\) with initial data in Lebesgue spaces \({L^2(\mathbb {R}^3)}\) or \({L^3(\mathbb {R}^3)}\) . We analyze the convergence of its solutions to a solution of the incompressible Navier–Stokes system as \({\epsilon \to 0}\) .
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Communicated by G.P. Galdi
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Rusin, W. Incompressible 3D Navier–Stokes Equations as a Limit of a Nonlinear Parabolic System. J. Math. Fluid Mech. 14, 383–405 (2012). https://doi.org/10.1007/s00021-011-0074-x
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DOI: https://doi.org/10.1007/s00021-011-0074-x