Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 5
184
Views
0
CrossRef citations to date
0
Altmetric
Articles

Existence of global strong solutions for Navier–Stokes equations with external force

&
Pages 997-1007 | Received 03 Jul 2011, Accepted 20 Nov 2011, Published online: 14 Dec 2011

References

  • Pedlosky , J . 1979 . Geophysical Fluid Dynamics , New York : Springer-Verlag .
  • Gerbeau , JF and Perthame , B . 2001 . Derivation of viscous Saint–Venant system for laminar shallow water, numerical validation . Discrete Contin. Dyn. Syst. Ser. B1 , 1 : 89 – 102 .
  • Marche , F . 2007 . Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects . Eur. J. Mech. B/Fluids. , 26 : 49 – 63 .
  • Guo , Z , Jiu , Q and Xin , Z . 2008 . Spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients . SIAM J. Math. Anal. , 39 : 1402 – 1427 .
  • Jiang , S , Xin , Z and Zhang , P . 2005 . Global weak solutions to 1D compressible isentropy Navier–Stokes with density-dependent viscosity . Methods Appl. Anal. , 12 : 239 – 252 .
  • Liu , T , Xin , Z and Yang , T . 1998 . Vacuum states for compressible flow . Discrete Contin. Dyn. Syst. , 4 : 1 – 32 .
  • Okada , M , Nečasoá , ŠM and Makino , T . 2002 . Free boundary problem for the equationof one-dimensional motion of compressible gas with density-dependent viscosity . Ann. Univ. Ferrara Sez. VII (N.S.) , 48 : 1 – 20 .
  • Vong , S , Yang , T and Zhu , C . 2003 . Compressible Navier–Stokes equations with degenerate viscosity coefficient and vacuum (II) . J. Differ. Eqns , 192 : 475 – 501 .
  • Yang , T , Yao , Z and Zhu , C . 2001 . Compressible Navier–Stokes equations with density-dependent viscosity and vacuum . Comm. PDEs , 26 : 965 – 981 .
  • Yang , T and Zhao , H . 2002 . A vacuum problem for the one-dimensional compressible Navier–Stokes equations with density-dependent viscosity . J. Differ. Eqns , 184 : 163 – 184 .
  • Yang , T and Zhu , C . 2002 . Compressible Navier–Stokes equations with degenerate viscosity coefficient and vacuum . Commu. Math. Phys. , 230 : 329 – 363 .
  • Mellet , A and Vasseur , A . 2008 . Existence and uniqueness of global strong solutions for one-dimensional compressible Navier–Stokes equations . SIAM J. Math. Anal. , 39 : 1344 – 1365 .
  • Jiu , Q and Xin , Z . 2008 . The Cauchy problem for 1D compressible flows with density-dependent viscosity coefficients . Kinet. Relat. Modeks. , 1 : 313 – 330 .
  • Jiu , Q , Wang , Y and Xin , Z . 2011 . Stability of rarefaction waves to the 1D compressible Navier–Stokes equations with density-dependent viscosity . Comm. PDEs , 36 : 602 – 634 .
  • Li , H , Li , J and Xin , Z . 2008 . Vanishing of vacuum states and blow-up phenomena of the compressible Navier–Stokes equations . Commun. Math. Phys. , 281 : 401 – 444 .
  • Lian , L , Guo , Z and Li , H . 2010 . Dynamical behaviours of vacuum states for 1D compressible Navier–Stokes equations . J. Differ. Eqns , 248 : 1926 – 1954 .
  • Bresch , D and Desjardins , B . 2003 . Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model . Comm. Math. Phys. , 238 : 211 – 223 .
  • Bresch , D and Desjardins , B . 2006 . On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier–Stokes models . J. Math. Pures Appl. , 86 : 362 – 368 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.