Showing papers by "Peter Constantin published in 2009"
TL;DR: Constantin and Wu as mentioned in this paper examined the regularity of weak solutions of quasi-geostrophic (QG) type equations with supercritical ( α 1 / 2 ) dissipation ( − Δ ) α.
111 citations
TL;DR: In this paper, the authors provide a proof of global regularity of solutions of coupled Navier-Stokes equations and Fokker-Planck equations in two spatial dimensions, in the absence of boundaries.
Abstract: We provide a proof of global regularity of solutions of coupled Navier-Stokes equations and Fokker-Planck equations, in two spatial dimensions, in the absence of boundaries. The proof yields a priori estimates for the growth of spatial
gradients.
42 citations
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TL;DR: In this paper, the authors discuss the regularity of solutions of 2D incompressible Navier-Stokes equations forced by singular forces, which leads naturally to bounded added stress and hence to W 1,1! <
Abstract: We discuss the regularity of solutions of 2D incompressible Navier-Stokes equations forced by singular forces. The problem is motivated by the study of complex fluids modeled by the Navier-Stokes equations coupled to a nonlinear Fokker-Planck equation describing microscopic corpora embedded in the fluid. This leads naturally to bounded added stress and hence to W 1,1 ! <
28 citations
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TL;DR: In this article, the authors provide a proof of global regularity of solutions of coupled Navier-Stokes equations and Fokker-Planck equations in two spatial dimensions, in the absence of boundaries.
Abstract: We provide a proof of global regularity of solutions of coupled Navier-Stokes equations and Fokker-Planck equations, in two spatial dimensions, in the absence of boundaries. The proof yields a priori estimates for the growth of spatial gradients.
11 citations