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Volumn 287, Issue 2, 2009, Pages 589-612

On the partial regularity of a 3D model of the Navier-Stokes equations

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EID: 61649125593     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0689-9     Document Type: Article
Times cited : (19)

References (40)
  • 1
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • 1
    • J.T. Beale T. Kato A. Majda 1984 Remarks on the breakdown of smooth solutions for the 3-D Euler equations Commun. Math. Phys. 94 1 61 66
    • (1984) Commun. Math. Phys. , vol.94 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.3
  • 2
    • 84990576577 scopus 로고
    • Partial regularity of suitable weak solutions of the Navier-Stokes equations
    • L. Caffarelli R. Kohn L. Nirenberg 1982 Partial regularity of suitable weak solutions of the Navier-Stokes equations Comm. Pure Appl. Math. 35 771 831
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 771-831
    • Caffarelli, L.1    Kohn, R.2    Nirenberg, L.3
  • 3
    • 36348955539 scopus 로고    scopus 로고
    • Global well-posedness of the three-dimensional primitive equations of large scale ocean and atmosphere dynamics
    • 1
    • C. Cao E.S. Titi 2007 Global well-posedness of the three-dimensional primitive equations of large scale ocean and atmosphere dynamics Ann. Math. 166 1 245 267
    • (2007) Ann. Math. , vol.166 , pp. 245-267
    • Cao, C.1    Titi, E.S.2
  • 4
    • 49949115307 scopus 로고    scopus 로고
    • Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations
    • published on March 14, 2008, doi: 10.1093/imrn/rnn016
    • Chen, C., Strain, R.M., Tsai, T., Yau, H.T.: Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations. Int. Math. Res. Not. 2008 (2008), published on March 14, 2008, doi: 10.1093/imrn/rnn016
    • (2008) Int. Math. Res. Not. 2008
    • Chen, C.1    Strain, R.M.2    Tsai, T.3    Yau, H.T.4
  • 6
    • 17444395218 scopus 로고    scopus 로고
    • Geometric properties and non-blowup of 3-D incompressible Euler flow
    • J. Deng T.Y. Hou X. Yu 2005 Geometric properties and non-blowup of 3-D incompressible Euler flow Commun. PDEs 30 225 243
    • (2005) Commun. PDEs , vol.30 , pp. 225-243
    • Deng, J.1    Hou, T.Y.2    Yu, X.3
  • 7
    • 31744438053 scopus 로고    scopus 로고
    • Improved geometric conditions for non-blowup of 3D incompressible Euler equation
    • J. Deng T.Y. Hou X. Yu 2006 Improved geometric conditions for non-blowup of 3D incompressible Euler equation Commun. PDEs 31 293 306
    • (2006) Commun. PDEs , vol.31 , pp. 293-306
    • Deng, J.1    Hou, T.Y.2    Yu, X.3
  • 9
    • 0042154193 scopus 로고    scopus 로고
    • translation in
    • translation in Russ. Math. Surveys 58(2) 211-250 (2003)
    • (2003) Russ. Math. Surveys , vol.58 , Issue.2 , pp. 211-250
  • 10
    • 61649113559 scopus 로고    scopus 로고
    • Fefferman, C.: http://www.claymath.org/millennium/Navier-Stokes-Equations
    • Fefferman, C.1
  • 11
    • 49949100775 scopus 로고    scopus 로고
    • Dynamic stability of the 3D axi-symmetric Navier-Stokes equations with swirl
    • 5
    • T.Y. Hou C. Li 2008 Dynamic stability of the 3D axi-symmetric Navier-Stokes equations with swirl CPAM 61 5 661 697
    • (2008) CPAM , vol.61 , pp. 661-697
    • Hou, T.Y.1    Li, C.2
  • 13
    • 49949114046 scopus 로고    scopus 로고
    • Global regularity of the 3D Axi-symmetric Navier-Stokes equations with anisotropic data
    • 9
    • T.Y. Hou Z. Lei C. Li 2008 Global regularity of the 3D Axi-symmetric Navier-Stokes equations with anisotropic data Commun. PDEs 33 9 1622 1637
    • (2008) Commun. PDEs , vol.33 , pp. 1622-1637
    • Hou, T.Y.1    Lei, Z.2    Li, C.3
  • 14
    • 84944818416 scopus 로고
    • Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen
    • E. Hopf 1951 Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen Math. Nachr. 4 213 231
    • (1951) Math. Nachr. , vol.4 , pp. 213-231
    • Hopf, E.1
  • 15
    • 9744237209 scopus 로고    scopus 로고
    • Regularity of axially symmetric flows in a half-space in three dimensions
    • 6
    • K. Kang 2004 Regularity of axially symmetric flows in a half-space in three dimensions SIAM J. Math. Anal. 35 6 1636 1643
    • (2004) SIAM J. Math. Anal. , vol.35 , pp. 1636-1643
    • Kang, K.1
  • 17
    • 0034389838 scopus 로고    scopus 로고
    • Bilinear estimates in BMO and the Navier-Stokes equations
    • 1
    • H. Kozono Y. Taniuchi 2000 Bilinear estimates in BMO and the Navier-Stokes equations Math. Z. 235 1 173 194
    • (2000) Math. Z. , vol.235 , pp. 173-194
    • Kozono, H.1    Taniuchi, Y.2
  • 20
    • 0042597992 scopus 로고
    • Unique global solvability of the three-dimensional Cauchy problem for the Navier-Stokes equations in the presence of axial symmetry
    • O.A. Ladyzhenskaya 1968 Unique global solvability of the three-dimensional Cauchy problem for the Navier-Stokes equations in the presence of axial symmetry (Russian) Zap. Nauv cn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 7 155 177
    • (1968) (Russian) Zap. Nauv Cn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , vol.7 , pp. 155-177
    • Ladyzhenskaya, O.A.1
  • 21
    • 0013198034 scopus 로고    scopus 로고
    • On partial regularity of suitable weak solutions to the three- dimensional Navier-Stokes equations
    • 4
    • O.A. Ladyzhenskaya G.A. Seregin 1999 On partial regularity of suitable weak solutions to the three- dimensional Navier-Stokes equations (English summary) J Math. Fluid Mech. 1 4 356 387
    • (1999) (English Summary) J Math. Fluid Mech. , vol.1 , pp. 356-387
    • Ladyzhenskaya, O.A.1    Seregin, G.A.2
  • 23
    • 51249193194 scopus 로고
    • Sur le mouvement d'un liquide visqueux emplissant l'espace
    • J. Leray 1934 Sur le mouvement d'un liquide visqueux emplissant l'espace Acta. Math. 63 193 248
    • (1934) Acta. Math. , vol.63 , pp. 193-248
    • Leray, J.1
  • 24
    • 0032344639 scopus 로고    scopus 로고
    • A new proof of the Caffarelli-Kohn-Nirenberg theorem
    • 3
    • F.-h. Lin 1998 A new proof of the Caffarelli-Kohn-Nirenberg theorem Comm. Pure Appl. Math. 51 3 241 257
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 241-257
    • Lin, F.-H.1
  • 25
    • 37849052235 scopus 로고    scopus 로고
    • Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows
    • 6
    • J.G. Liu W.C. Wang 2006 Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows SINUM 44 6 2456 2480
    • (2006) SINUM , vol.44 , pp. 2456-2480
    • Liu, J.G.1    Wang, W.C.2
  • 27
    • 27144458223 scopus 로고    scopus 로고
    • On the role of the convection term in the equations of motion of incompressible fluid
    • 10
    • H. Okamoto K. Ohkitani 2005 On the role of the convection term in the equations of motion of incompressible fluid J. Phys. Soc. Japan 74 10 2737 2742
    • (2005) J. Phys. Soc. Japan , vol.74 , pp. 2737-2742
    • Okamoto, H.1    Ohkitani, K.2
  • 28
    • 0001307388 scopus 로고
    • Un teorema di unicità per le equazioni di Navier-Stokes
    • 4
    • G. Prodi 1959 Un teorema di unicità per le equazioni di Navier-Stokes Ann. Mat. Pura Appl. 48 4 173 182
    • (1959) Ann. Mat. Pura Appl. , vol.48 , pp. 173-182
    • Prodi, G.1
  • 29
    • 84972517978 scopus 로고
    • Partial regularity of solutions to the Navier-Stokes equations
    • 2
    • V. Scheffer 1976 Partial regularity of solutions to the Navier-Stokes equations Pac. J. Math. 66 2 535 552
    • (1976) Pac. J. Math. , vol.66 , pp. 535-552
    • Scheffer, V.1
  • 30
    • 0002117826 scopus 로고
    • Hausdorff measure and the Navier-Stokes equations
    • 2
    • V. Scheffer 1977 Hausdorff measure and the Navier-Stokes equations Commun. Math. Phys. 55 2 97 112
    • (1977) Commun. Math. Phys. , vol.55 , pp. 97-112
    • Scheffer, V.1
  • 31
    • 0001881423 scopus 로고
    • The Navier-Stokes equations on a bounded domain
    • 1
    • V. Scheffer 1980 The Navier-Stokes equations on a bounded domain Commun. Math. Phys. 73 1 1 42
    • (1980) Commun. Math. Phys. , vol.73 , pp. 1-42
    • Scheffer, V.1
  • 32
    • 0043106636 scopus 로고
    • Boundary regularity for the Navier-Stokes equations
    • 2
    • V. Scheffer 1982 Boundary regularity for the Navier-Stokes equations Commun. Math. Phys. 85 2 275 299
    • (1982) Commun. Math. Phys. , vol.85 , pp. 275-299
    • Scheffer, V.1
  • 33
    • 0000169262 scopus 로고
    • On the interior regularity of weak solutions of the Navier-Stokes equations
    • J. Serrin 1962 On the interior regularity of weak solutions of the Navier-Stokes equations Arch. Rat. Mech. Anal. 9 187 195
    • (1962) Arch. Rat. Mech. Anal. , vol.9 , pp. 187-195
    • Serrin, J.1
  • 34
    • 0001807443 scopus 로고
    • The initial value problem for the Navier-Stokes equations
    • Madison WI: Univ. of Wisconsin Press
    • Serrin, J.: The initial value problem for the Navier-Stokes equations. In: Nonlinear Problems. Madison WI: Univ. of Wisconsin Press, pp. 69-98, 1963
    • (1963) Nonlinear Problems , pp. 69-98
    • Serrin, J.1
  • 35
    • 84990553438 scopus 로고
    • On partial regularity results for the Navier-Stokes equations
    • 4
    • M. Struwe 1988 On partial regularity results for the Navier-Stokes equations Comm. Pure Appl. Math. 41 4 437 458
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 437-458
    • Struwe, M.1
  • 37
    • 0042096896 scopus 로고
    • Axially symmetric flows of ideal and viscous fluids filling the whole space
    • (Russian)
    • Ukhovskii, M.R., Iudovich, V.I.: Axially symmetric flows of ideal and viscous fluids filling the whole space. Prikl. Mat. Meh. 32, 59-69 (1968) (Russian)
    • (1968) Prikl. Mat. Meh. , vol.32 , pp. 59-69
    • Ukhovskii, R.M.1    Iudovich, I.V.2
  • 38
    • 0042598003 scopus 로고
    • translated as
    • translated as J. Appl. Math. Mech. 32, 52-61 (1968)
    • (1968) J. Appl. Math. Mech. , vol.32 , pp. 52-61
  • 39
    • 21844513548 scopus 로고
    • n
    • (English summary) A Chinese summary appears in
    • n. (English summary) A Chinese summary appears in Chinese Ann. Math. Ser. A 16(6), (1995). 797
    • (1995) Chinese Ann. Math. Ser. A , vol.16 , Issue.6 , pp. 797
    • Beirãoda Veiga, H.1
  • 40


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.