메뉴 건너뛰기




Volumn 3, Issue 2, 2010, Pages 185-197

Loss of smoothness and energy conserving rough weak solutions for the 3D euler equations

Author keywords

Kelvin Helmholtz; Loss of smoothness for the three dimensional Euler equations; Onsager's conjecture and conservation of energy for Euler equations; Vortex sheet

Indexed keywords


EID: 79951824256     PISSN: 19371632     EISSN: 19371179     Source Type: Journal    
DOI: 10.3934/dcdss.2010.3.185     Document Type: Article
Times cited : (66)

References (31)
  • 3
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3D Euler equations
    • J. T. Beale, T. Kato and A. Majda, Remarks on the breakdown of smooth solutions for the 3D 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
    • 0001747831 scopus 로고
    • Singular solutions and ill-posedness for the evolution of vortex sheets
    • R. Caflisch and O. Orellana, Singular solutions and ill-posedness for the evolution of vortex sheets, SIAM J. Math. Anal., 20 (1989), 293-307.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 293-307
    • Caflisch, R.1    Orellana, O.2
  • 6
    • 45149096278 scopus 로고    scopus 로고
    • Energy conservation and On-sager's conjecture for the Euler equations
    • A. Cheskidov, P. Constantin, S. Friedlander and R. Shvydkoy, Energy conservation and On-sager's conjecture for the Euler equations, Nonlinearity, 21 (2008), 1233-1252.
    • (2008) Nonlinearity , vol.21 , pp. 1233-1252
    • Cheskidov, A.1    Constantin, P.2    Friedlander, S.3    Shvydkoy, R.4
  • 7
    • 41849149355 scopus 로고    scopus 로고
    • On the Euler equations of incompressible fluids
    • P. Constantin, On the Euler equations of incompressible fluids, Bulletin, AMS, 44 (2007), 603-621.
    • (2007) Bulletin, AMS , vol.44 , pp. 603-621
    • Constantin, P.1
  • 8
    • 21844522201 scopus 로고
    • Onsager's conjecture on the Energy Conservation for Solutions of Euler's equation
    • P. Constantin, W. E and E. S. Titi, Onsager's conjecture on the Energy Conservation for Solutions of Euler's equation, Comm. Math. Phys., 165 (1994), 207-209.
    • (1994) Comm. Math. Phys. , vol.165 , pp. 207-209
    • Constantin W E, P.1    Titi, E.S.2
  • 10
    • 84968509708 scopus 로고
    • Existence de nappes de tourbillon en dimension deux
    • J.-M. Delort, Existence de nappes de tourbillon en dimension deux, J. Amer. Math. Soc., 4 (1991), 553-586.
    • (1991) J. Amer. Math. Soc. , vol.4 , pp. 553-586
    • Delort, J.-M.1
  • 11
    • 0000863080 scopus 로고
    • Oscillations and concentrations in weak solutions of the incompressible fluid equations
    • R. DiPerna and A. Majda, Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys., 108 (1987), 667-689.
    • (1987) Comm. Math. Phys. , vol.108 , pp. 667-689
    • Diperna, R.1    Majda, A.2
  • 12
    • 0013229088 scopus 로고
    • Global vortex sheet solutions of Euler equations in the plane
    • J. Duchon and R. Robert, Global vortex sheet solutions of Euler equations in the plane, J. Differential Equations, 73 (1988), 215-224.
    • (1988) J. Differential Equations , vol.73 , pp. 215-224
    • Duchon, J.1    Robert, R.2
  • 13
    • 0002205604 scopus 로고
    • Energy dissipation without viscosity in ideal hydrodynamics, I. Fourier analysis and local energy transfer
    • G. L. Eyink, Energy dissipation without viscosity in ideal hydrodynamics, I. Fourier analysis and local energy transfer, Phys. D, 78 (1994), 222-240.
    • (1994) Phys. D , vol.78 , pp. 222-240
    • Eyink, G.L.1
  • 14
    • 0023451072 scopus 로고
    • Computation of vortex sheet roll-up in Trefftz plane
    • R. Krasny, Computation of vortex sheet roll-up in Trefftz plane, J. Fluid Mech., 184 (1987), 123-155. (Pubitemid 18536609)
    • (1987) Journal of Fluid Mechanics , vol.184 , pp. 123-155
    • Krasny Robert1
  • 15
    • 17044425556 scopus 로고    scopus 로고
    • Régularité du problème de Kelvin-Helmholtz pour l'équation d'euler 2D
    • DOI 10.1051/cocv:2002052
    • G. Lebeau, Egularit'e du probl̀eme de Kelvin-Helmholtz pour l'́equation d'Euler 2d, ESAIM Control Optim. Calc. Var., 8 (2002), 801-825 (electronic). (Pubitemid 47616049)
    • (2002) ESAIM - Control, Optimisation and Calculus of Variations , vol.8 , pp. 801-825
    • Lebeau, G.1
  • 16
    • 0002294455 scopus 로고    scopus 로고
    • of Chapman & Hall/CRC Research Notes in Mathematics, Chapman & Hall/CRC, Boca Raton, FL
    • P. G. Lemaríe-Rieusset, "Recent Developments in the Navier-Stokes Problem," vol. 431 of Chapman & Hall/CRC Research Notes in Mathematics, Chapman & Hall/CRC, Boca Raton, FL, 2002.
    • (2002) Recent Developments in the Navier-Stokes Problem , vol.431
    • Lemaríe-Rieusset, P.G.1
  • 17
    • 0009002721 scopus 로고
    • Uber einige existenz problem der hydrodynamik homogener unzusam-mendrückbarer, reibunglosser Flüssikeiten und die Helmholtzschen wirbelsalitze
    • L. Lichtenstein, Uber einige existenz problem der hydrodynamik homogener unzusam-mendrückbarer, reibunglosser Flüssikeiten und die Helmholtzschen wirbelsalitze, Math. Z., 23 (1925), 89-154.
    • (1925) Math. Z. , vol.23 , pp. 89-154
    • Lichtenstein, L.1
  • 18
    • 0003628399 scopus 로고    scopus 로고
    • Incompressible Models, Oxford Lecture Series in Mathematics and its Applications, 3, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York
    • P. L. Lions, "Mathematical Topics in Fluid Mechanics," Volume 1, "Incompressible Models," Oxford Lecture Series in Mathematics and its Applications, 3, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1996.
    • (1996) Mathematical Topics in Fluid Mechanics , vol.1
    • Lions, P.L.1
  • 19
    • 47049087667 scopus 로고    scopus 로고
    • A criterion for the equivalence of the Birkhoff-Rott and Euler description of vortex sheet evolution
    • (electronic)
    • M. C. Lopes Filho, H. J. Nussenzveig Lopes and S. Schochet, A criterion for the equivalence of the Birkhoff-Rott and Euler description of vortex sheet evolution, Trans. Amer. Math. Soc., 359 (2007), 4125-4142 (electronic).
    • (2007) Trans. Amer. Math. Soc. , vol.359 , pp. 4125-4142
    • Lopes Filho, M.C.1    Nussenzveig Lopes, H.J.2    Schochet, S.3
  • 20
    • 0040438755 scopus 로고    scopus 로고
    • Existence of vortex sheets with reflection symmetry in two space dimensions
    • M. C. Lopes Filho, H. J. Nussenzveig Lopes and Z. Xin, Existence of vortex sheets with reflection symmetry in two space dimensions, Arch. Ration. Mech. Anal., 158 (2001), 235-257.
    • (2001) Arch. Ration. Mech. Anal. , vol.158 , pp. 235-257
    • Lopes Filho, M.C.1    Nussenzveig Lopes, H.J.2    Xin, Z.3
  • 21
    • 0242618501 scopus 로고    scopus 로고
    • Vorticity and incompressible flow
    • Cambridge University Press, Cambridge
    • A. Majda and A. Bertozzi, "Vorticity and Incompressible Flow," Cambridge Texts in Applied Mathematics, 27 Cambridge University Press, Cambridge, 2002.
    • (2002) Cambridge Texts in Applied Mathematics , vol.27
    • Majda, A.1    Bertozzi, A.2
  • 24
    • 8744277357 scopus 로고    scopus 로고
    • Existence of solution for the Euler equations in a critical Besov space
    • H. C. Pak and Y. J. Park, Existence of solution for the Euler equations in a critical Besov space, Communications PDEs, 29 (2004), 1149-1166.
    • (2004) Communications PDEs , vol.29 , pp. 1149-1166
    • Pak, H.C.1    Park, Y.J.2
  • 25
    • 0001768220 scopus 로고
    • An inviscid flow with compact support in space-time
    • V. Scheffer, An inviscid flow with compact support in space-time, J. of Geom. Anal., 3 (1993), 343-401.
    • (1993) J. of Geom. Anal. , vol.3 , pp. 343-401
    • Scheffer, V.1
  • 26
    • 0031491102 scopus 로고    scopus 로고
    • On the nonuniqueness of weak solutions of the Euler equations
    • A. Shnirelman, On the nonuniqueness of weak solutions of the Euler equations, Comm. Pure Appl. Math., 50 (1997), 1261-1286.
    • (1997) Comm. Pure Appl. Math. , vol.50 , pp. 1261-1286
    • Shnirelman, A.1
  • 27
    • 53349162103 scopus 로고    scopus 로고
    • On the energy of inviscid singular flows
    • R. Shvydkoy, On the energy of inviscid singular flows, J. Math. Anal. Appl., 349 (2009), 583-595.
    • (2009) J. Math. Anal. Appl. , vol.349 , pp. 583-595
    • Shvydkoy, R.1
  • 28
    • 0038247451 scopus 로고
    • Finite time analyticity for the two-and three-dimensional Kelvin-Helmholtz instability
    • C. Sulem, P.-L. Sulem, C. Bardos and U. Frisch, Finite time analyticity for the two-and three-dimensional Kelvin-Helmholtz instability, Comm. Math. Phys., 80 (1981), 485-516.
    • (1981) Comm. Math. Phys. , vol.80 , pp. 485-516
    • Sulem, C.1    Sulem, P.-L.2    Bardos, C.3    Frisch, U.4
  • 29
    • 84864622522 scopus 로고
    • of Monographs in Mathematics, Birkḧauser Verlag, Basel
    • H. Triebel, "Theory of Function Spaces," vol. 78 of Monographs in Mathematics, Birkḧauser Verlag, Basel, 1983.
    • (1983) Theory of Function Spaces , vol.78
    • Triebel, H.1
  • 30
    • 33745626744 scopus 로고    scopus 로고
    • Mathematical analysis of vortex sheets
    • DOI 10.1002/cpa.20110
    • S. Wu, Mathematical analysis of vortex sheets, Comm. Pure Appl. Math., 59 (2006), 1065-1206. (Pubitemid 43988294)
    • (2006) Communications on Pure and Applied Mathematics , vol.59 , Issue.8 , pp. 1065-1206
    • Wu, S.1
  • 31
    • 0345801447 scopus 로고    scopus 로고
    • On the loss of smoothness of the solutions of the Euler equations and the inherent instability of flows of an ideal fluid
    • V. I. Yudovich, On the loss of smoothness of the solutions of the Euler equations and the inherent instability of flows of an ideal fluid, Chaos, 10 (2000), 705-719.
    • (2000) Chaos , vol.10 , pp. 705-719
    • Yudovich, V.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.