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Original Articles

Local solvability of an inverse problem to the density-dependent Navier–Stokes equations

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Pages 1255-1265 | Received 16 Mar 2008, Accepted 26 Jul 2008, Published online: 23 Dec 2008

Reference s

  • Kazhikov , AV . 1974 . Solvability of the initial-boundary value problem for the equations of the motion of an inhomogeneous viscous incompressible fluid . Dokl. Akad. Nauh. , 216 : 1008 – 1010 .
  • Ladyzhenskaya , OA and Solonnikov , VA . 1978 . Unique solvability of an initial and boundary value problem for viscous incompressible nonhomogeneous fluids . J. Soviet. Math. , 9 : 697 – 749 .
  • Antontsev , SN , Kazhikov , AV and Monakhov , VN . 1990 . Boundary Value Problem in Mechanics of Nonhomogeneous Fluids , Amsterdam : North-Holland Publishing Co. .
  • Simon , J . 1990 . Nonhomogeneous viscous incompressible fluids: Existence of velocity, density and pressure . SIAM J. Math. Anal. , 21 ( 5 ) : 1093 – 1117 .
  • Lions , PL . 1996 . Mathematical topics in fluid mechanics, vol.1: incompressible Models, in Oxford Lecture Series in Mathematics and Its Applications, Vol.10 , New York : The Clarendon Press, Oxford University Press .
  • Choe , HJ and Kim , H . 2003 . Strong solutions of the Navier–Stokes equations for nonhomogeneous incompressible fluids . Comm. Partial Diff. Eqns. , 28 : 1183 – 1201 .
  • Cho , Y and Kim , H . 2004 . Unique solvability for the density-dependent Navier–Stokes equations . Nonlinear Anal. TMA , 59 : 465 – 489 .
  • Danchin , R . 2003 . Density-dependent incompressible viscous fluids in critical spaces . Proc. R. Soc. Edingburgh , 133A : 1311 – 1334 .
  • Prilepko , AI , Orlovsky , DG and Vasin , IA . 2000 . Methods for Solving Inverse Problems in Mathematical Physics , New York : Marcel Dekker, Inc. .
  • Novotný , A and Straškraba , I . 2004 . Introduction to the Mathematical Theory of Compressible Flow , Oxford : Oxford University Press .
  • Temam , R . 1977 . Theory and Numerical Analysis. Studies in Mathematics and its Applications, Vol. 2 , Amsterdam, New York, Oxford : North-Holland Publishing Co. .

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