메뉴 건너뛰기




Volumn 190, Issue 1, 2003, Pages 39-63

On blow-up criteria of smooth solutions to the 3-D Euler equations in a bounded domain

Author keywords

Blow up of smooth solutions; bmo

Indexed keywords


EID: 0038706224     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00013-5     Document Type: Article
Times cited : (36)

References (37)
  • 1
    • 84980080664 scopus 로고
    • Estimates over the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
    • S. Agmon, A. Douglis, L. Nirenberg, Estimates over the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Commun. Pure Appl. Math. 17 (1964) 35-92.
    • (1964) Commun. Pure Appl. Math. , vol.17 , pp. 35-92
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 2
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • J.T. Beale, T. Kato, A. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Commun. Math. Phys. 94 (1984) 61-66.
    • (1984) Commun. Math. Phys. , vol.94 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.3
  • 4
    • 49149142420 scopus 로고
    • Nonlinear Schrödinger evolution equations
    • H. Brezis, T. Gallouet, Nonlinear Schrödinger evolution equations, Nonlinear Anal. TMA 4 (1980) 677-681.
    • (1980) Nonlinear Anal. TMA , vol.4 , pp. 677-681
    • Brezis, H.1    Gallouet, T.2
  • 5
    • 0000628903 scopus 로고
    • A note on limiting cases of Sobolev embedding and convolution inequalities
    • H. Brezis, S. Wainger, A note on limiting cases of Sobolev embedding and convolution inequalities, Commun. Partial Differential Equations 5 (1987) 773-789.
    • (1987) Commun. Partial Differential Equations , vol.5 , pp. 773-789
    • Brezis, H.1    Wainger, S.2
  • 7
    • 0028388187 scopus 로고
    • Geometric statistics in turbulence
    • P. Constantin, Geometric statistics in turbulence, SIAM Rev. 36 (1994) 73-98.
    • (1994) SIAM Rev. , vol.36 , pp. 73-98
    • Constantin, P.1
  • 8
    • 0038205254 scopus 로고
    • Geometric and analytic studies in turbulences
    • L. Sirovich (Ed.), Appl. Math. Sciences Springer, Berlin
    • P. Constantin, Geometric and analytic studies in turbulences, in: L. Sirovich (Ed.), Trends and Perspectives in Applied Mathematics, Appl. Math. Sciences, Vol. 100, Springer, Berlin, 1994.
    • (1994) Trends and Perspectives in Applied Mathematics , vol.100
    • Constantin, P.1
  • 9
    • 0038543972 scopus 로고
    • Active Scalars and the Euler Equation
    • P. Constantin, Active Scalars and the Euler Equation, Tatra Mountain Math. Publ. 4 (1994) 25-38.
    • (1994) Tatra Mountain Math. Publ. , vol.4 , pp. 25-38
    • Constantin, P.1
  • 10
    • 0000385525 scopus 로고    scopus 로고
    • Geometric constraints on potentially singular solutions for the 3-D Euler equations
    • P. Constantin, C. Fefferman, A. Majda, Geometric constraints on potentially singular solutions for the 3-D Euler equations, Commun. Partial Differential Equations 21 (1996) 559-571.
    • (1996) Commun. Partial Differential Equations , vol.21 , pp. 559-571
    • Constantin, P.1    Fefferman, C.2    Majda, A.3
  • 11
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the motion of an incompressible fluid
    • D.G. Ebin, J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. 92 (1970) 102-163.
    • (1970) Ann. of Math. , vol.92 , pp. 102-163
    • Ebin, D.G.1    Marsden, J.2
  • 12
    • 0037867565 scopus 로고
    • An alternative proof of the Brezis-Wainger inequality
    • H. Engler, An alternative proof of the Brezis-Wainger inequality, Commun. Partial Differential Equations 14 (4) (1989) 541-544.
    • (1989) Commun. Partial Differential Equations , vol.14 , Issue.4 , pp. 541-544
    • Engler, H.1
  • 13
    • 21144480338 scopus 로고
    • On the blow-up of solutions of 3-D Euler equations in a bounded domain
    • A.B. Ferrari, On the blow-up of solutions of 3-D Euler equations in a bounded domain, Commun. Math. Phys. 155 (1993) 277-294.
    • (1993) Commun. Math. Phys. , vol.155 , pp. 277-294
    • Ferrari, A.B.1
  • 15
    • 0003134154 scopus 로고
    • Nonlinear evolution equations and the Euler flow
    • T. Kato, C.Y. Lai, Nonlinear evolution equations and the Euler flow, J. Funct. Anal. 56 (1984) 15-28.
    • (1984) J. Funct. Anal. , vol.56 , pp. 15-28
    • Kato, T.1    Lai, C.Y.2
  • 17
    • 84990617895 scopus 로고
    • Commutator estimates and the Euler and Navier-Stokes equations
    • T. Kato, G. Ponce, Commutator estimates and the Euler and Navier-Stokes equations, Commun. Pure Appl. Math. 41 (1988) 891-907.
    • (1988) Commun. Pure Appl. Math. , vol.41 , pp. 891-907
    • Kato, T.1    Ponce, G.2
  • 18
    • 0012945781 scopus 로고    scopus 로고
    • The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
    • H. Kozono, T. Ogawa, Y. Taniuchi, The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations, Math. Z. 242 (2002) 251-278.
    • (2002) Math. Z. , vol.242 , pp. 251-278
    • Kozono, H.1    Ogawa, T.2    Taniuchi, Y.3
  • 19
    • 0034389838 scopus 로고    scopus 로고
    • Bilinear estimates in BMO and to the Navier-Stokes equations
    • H. Kozono, Y. Taniuchi, Bilinear estimates in BMO and to the Navier-Stokes equations, Math. Z. 235 (2000) 173-194.
    • (2000) Math. Z. , vol.235 , pp. 173-194
    • Kozono, H.1    Taniuchi, Y.2
  • 20
    • 0034348203 scopus 로고    scopus 로고
    • Limiting case of the Sobolev inequality in BMO, with application to the Euler equations
    • H. Kozono, Y. Taniuchi, Limiting case of the Sobolev inequality in BMO, with application to the Euler equations, Commun. Math. Phys. 214 (2000) 191-200.
    • (2000) Commun. Math. Phys. , vol.214 , pp. 191-200
    • Kozono, H.1    Taniuchi, Y.2
  • 21
    • 0037867563 scopus 로고    scopus 로고
    • Remarks on uniqueness and blow-up criterion to the Euler equations in the generalized Besov spaces
    • T. Ogawa, Y. Taniuchi, Remarks on uniqueness and blow-up criterion to the Euler equations in the generalized Besov spaces, J. Korean Math. Soc. 37 (2000) 1007-1029.
    • (2000) J. Korean Math. Soc. , vol.37 , pp. 1007-1029
    • Ogawa, T.1    Taniuchi, Y.2
  • 22
    • 3042764963 scopus 로고    scopus 로고
    • A note on blow-up criterion to the 3-D Euler equations in a bounded domain
    • in press
    • T. Ogawa, Y. Taniuchi, A note on blow-up criterion to the 3-D Euler equations in a bounded domain, J. Math. Fluid Mech., in press.
    • J. Math. Fluid Mech.
    • Ogawa, T.1    Taniuchi, Y.2
  • 23
    • 0038205249 scopus 로고
    • Abstract quasilinear evolution equations of hyperbolic type, with applications
    • Nonlinear Analysis and Applications (Warsaw, 1994)
    • N. Okazawa, Abstract quasilinear evolution equations of hyperbolic type, with applications, Nonlinear Analysis and Applications (Warsaw, 1994), GAKUTO Internat. Ser. Math. Sci. Appl. 7 (1995) 303-307.
    • (1995) GAKUTO Internat. Ser. Math. Sci. Appl. , vol.7 , pp. 303-307
    • Okazawa, N.1
  • 24
    • 0037867554 scopus 로고    scopus 로고
    • The Euler Equation on a bounded domain as a quasilinear evolution equation
    • N. Okazawa, The Euler Equation on a bounded domain as a quasilinear evolution equation, Commun. Appl. Nonlinear Anal. 3 (1996) 107-113.
    • (1996) Commun. Appl. Nonlinear Anal. , vol.3 , pp. 107-113
    • Okazawa, N.1
  • 25
    • 0000506513 scopus 로고
    • On critical cases of Sobolev's inequalities
    • T. Ozawa, On critical cases of Sobolev's inequalities, J. Funct. Anal. 127 (1995) 259-269.
    • (1995) J. Funct. Anal. , vol.127 , pp. 259-269
    • Ozawa, T.1
  • 26
    • 0009268557 scopus 로고
    • A continuation principle for the 3-D Euler equations for incompressible fluids in a bounded domain
    • T. Shirota, T. Yanagisawa, A continuation principle for the 3-D Euler equations for incompressible fluids in a bounded domain, Proc. Jpn. Acad. Ser. A 69 (1993) 77-82.
    • (1993) Proc. Jpn. Acad. Ser. A , vol.69 , pp. 77-82
    • Shirota, T.1    Yanagisawa, T.2
  • 27
    • 0037867566 scopus 로고
    • On Green's matrices for elliptic boundary value problems I
    • V.A. Solonnikov, On Green's matrices for elliptic boundary value problems I, Trudy Mat. Inst. Steklov 110 (1970) 123-170.
    • (1970) Trudy Mat. Inst. Steklov , vol.110 , pp. 123-170
    • Solonnikov, V.A.1
  • 28
    • 0038543975 scopus 로고
    • On Green's matrices for elliptic boundary value problems II
    • V.A. Solonnikov, On Green's matrices for elliptic boundary value problems II, Trudy Mat. Inst. Steklov 116 (1971) 187-226.
    • (1971) Trudy Mat. Inst. Steklov , vol.116 , pp. 187-226
    • Solonnikov, V.A.1
  • 29
    • 0004136765 scopus 로고
    • Harmonic Analysis
    • Princeton University Press, Princeton, NJ
    • E.M. Stein, Harmonic Analysis, Princeton University Press, Princeton, NJ, 1993.
    • (1993)
    • Stein, E.M.1
  • 30
    • 66149147603 scopus 로고    scopus 로고
    • A note on the blow-up criterion for the inviscid 2-D Boussinesq equations
    • preprint
    • Y. Taniuchi, A note on the blow-up criterion for the inviscid 2-D Boussinesq equations, preprint.
    • Taniuchi, Y.1
  • 31
    • 0003434854 scopus 로고
    • Pseudodifferential Operators and Nonlinear PDE, Progress of Mathematics
    • Birkhäuser, Boston, Basel, Berlin
    • M.E. Taylor, Pseudodifferential Operators and Nonlinear PDE, Progress of Mathematics, Birkhäuser, Boston, Basel, Berlin, 1991.
    • (1991)
    • Taylor, M.E.1
  • 32
    • 0039495612 scopus 로고
    • On the Euler equations of incompressible perfect fluids
    • R. Temam, On the Euler equations of incompressible perfect fluids, J. Fanct. Anal. 20 (1975) 32-43.
    • (1975) J. Fanct. Anal. , vol.20 , pp. 32-43
    • Temam, R.1
  • 33
    • 0004058897 scopus 로고
    • Theory of Function Spaces II
    • Birkhäuser, Basel
    • H. Triebel, Theory of Function Spaces II, Birkhäuser, Basel, 1992.
    • (1992)
    • Triebel, H.1
  • 34
    • 0033472885 scopus 로고    scopus 로고
    • Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type
    • M. Vishik, Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type, Ann. Sci. École Norm. Sup. 32 (1999) 769-812.
    • (1999) Ann. Sci. École Norm. Sup. , vol.32 , pp. 769-812
    • Vishik, M.1
  • 35
    • 0034349423 scopus 로고    scopus 로고
    • Incompressible flows of an ideal fluid with unbounded vorticity
    • M. Vishik, Incompressible flows of an ideal fluid with unbounded vorticity, Commun. Math. Phys. 213 (2000) 697-731.
    • (2000) Commun. Math. Phys. , vol.213 , pp. 697-731
    • Vishik, M.1
  • 36
    • 0002131061 scopus 로고
    • Uniqueness theorem for the basic nonstationary problem in the dynamics of an ideal incompressible fluid
    • V.I. Yudovich, Uniqueness theorem for the basic nonstationary problem in the dynamics of an ideal incompressible fluid, Math. Res. Lett. 2 (1995) 27-39.
    • (1995) Math. Res. Lett. , vol.2 , pp. 27-39
    • Yudovich, V.I.1
  • 37
    • 0037867564 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-d Euler equations in a bounded domain
    • W.M. Zajaczkowski, Remarks on the breakdown of smooth solutions for the 3-d Euler equations in a bounded domain, Bull. Polish Acad. Sci. Math. 37 (1989) 169-181.
    • (1989) Bull. Polish Acad. Sci. Math. , vol.37 , pp. 169-181
    • Zajaczkowski, W.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.