Publication Cover
Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 4
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Original Articles

On the well-posedness of incompressible flow in porous media with supercritical diffusion

Pages 547-561 | Received 09 Sep 2008, Accepted 17 Mar 2009, Published online: 16 Jun 2009

References

  • Nield , DA and Bejan , A . 1999 . Convection in Porous Media , New Jersey : Springer-Verlag .
  • Castro , A , Córdoba , D , Gancedo , F and Orive , R . Incompressible flow in porous media with fractional diffusion . (preprint 2008). Available at http://arxiv.org/abs/0806.1180
  • Córdoba , D , Gancedo , F and Orive , R . 2007 . Analytical behaviour of the two-dimensional incompressible flow in porous media . J. Math. Phys. , 48 : 1 – 19 .
  • Abidi , H and Hmidi , T . On the global well posedness of the critical quasi-geostrophic equation . SIAM J. Math. Anal., to appear. Available at http://arxiv.org/abs/math/0702215
  • Caffarelli , L and Vasseur , V . Drift diffusion equations with fractional diffusion and the quasi-geostrophic equations . Annals of Math. , to appear. Available at http://arxiv.org/abs/math/0608447
  • Chen , Q , Miao , C and Zhang , Z . 2007 . A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation . Comm. Math. Phys. , 271 : 821 – 838 .
  • Hmidi , T and Kernaani , S . 2007 . Global solutions of the supercritical 2D dissipative quasi-geostrophic equation . Adv. Math. , 214 : 618 – 638 .
  • Ju , N . 2004 . Existence and uniqueness of solution to the dissipative 2D quasi-geostrophic equations in the Sobelov space . Comm. Math. Phys. , 251 : 365 – 376 .
  • Kislev , A , Nazarov , F and Volberg , A . 2007 . Global well-posedness for the critical 2D dissipative quasi-geostrophic equation . Invent. Math. , 167 : 445 – 453 .
  • Chemin , J-Y . 1998 . Perfect incompressible fluids , Oxford : Clarendon Press .
  • J. Duoandikoetxea, Fourier Analysis, (Translated and revised by D. Cruz-Uribe). GSM vol.29, AMS, Providence, RI, 2001
  • Córdoba , A and Córdoba , D . 2004 . A maximum principle applied to the quasi-geostrophic equations . Comm. Math. Phys. , 249 : 511 – 528 .
  • Danchin , R . 2003 . Density-dependent incompressible viscous fluids in critical spaces . Proc. Roy. Soc. Ed , 133 : 1311 – 1334 .

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