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Volumn 217, Issue 6, 2008, Pages 2563-2568

Blow-up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation

Author keywords

Blow up; Hilbert transform; Quasi geostrophic equations; Supercritical

Indexed keywords


EID: 39749098738     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2007.11.002     Document Type: Article
Times cited : (67)

References (12)
  • 1
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • Beale J.T., Kato T., and Majda A. Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm. Math. Phys. 94 1 (1984) 61-66
    • (1984) Comm. Math. Phys. , vol.94 , Issue.1 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.3
  • 3
    • 16244382542 scopus 로고    scopus 로고
    • Finite time singularities in a 1D model of the quasi-geostrophic equation
    • Chae D., Córdoba A., Córdoba D., and Fontelos M.A. Finite time singularities in a 1D model of the quasi-geostrophic equation. Adv. Math. 194 (2005) 203-223
    • (2005) Adv. Math. , vol.194 , pp. 203-223
    • Chae, D.1    Córdoba, A.2    Córdoba, D.3    Fontelos, M.A.4
  • 4
    • 84990556249 scopus 로고
    • A simple one-dimensional model for the three-dimensional vorticity
    • Constantin P., Lax P., and Majda A. A simple one-dimensional model for the three-dimensional vorticity. Comm. Pure Appl. Math. 38 (1985) 715-724
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 715-724
    • Constantin, P.1    Lax, P.2    Majda, A.3
  • 5
    • 33745899606 scopus 로고    scopus 로고
    • Formation of singularities for a transport equation with nonlocal velocity
    • Córdoba A., Córdoba D., and Fontelos M.A. Formation of singularities for a transport equation with nonlocal velocity. Ann. of Math. 162 3 (2005) 1375-1387
    • (2005) Ann. of Math. , vol.162 , Issue.3 , pp. 1375-1387
    • Córdoba, A.1    Córdoba, D.2    Fontelos, M.A.3
  • 6
    • 0006605544 scopus 로고
    • On a one-dimensional model for the three-dimensional vorticity equation
    • De Gregorio S. On a one-dimensional model for the three-dimensional vorticity equation. J. Statist. Phys. 59 (1990) 1251-1263
    • (1990) J. Statist. Phys. , vol.59 , pp. 1251-1263
    • De Gregorio, S.1
  • 7
    • 0030269759 scopus 로고    scopus 로고
    • A partial differential equation arising in a 1D model for the 3D vorticity equation
    • De Gregorio S. A partial differential equation arising in a 1D model for the 3D vorticity equation. Math. Methods Appl. Sci. 19 (1996) 1233-1255
    • (1996) Math. Methods Appl. Sci. , vol.19 , pp. 1233-1255
    • De Gregorio, S.1
  • 8
    • 39749187247 scopus 로고    scopus 로고
    • H. Dong, Well-posedness for a transport equation with nonlocal velocity, preprint
    • H. Dong, Well-posedness for a transport equation with nonlocal velocity, preprint
  • 9
    • 33846785446 scopus 로고    scopus 로고
    • Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
    • Kiselev A., Nazarov F., and Volberg A. Global well-posedness for the critical 2D dissipative quasi-geostrophic equation. Invent. Math. 167 3 (2007) 445-453
    • (2007) Invent. Math. , vol.167 , Issue.3 , pp. 445-453
    • Kiselev, A.1    Nazarov, F.2    Volberg, A.3
  • 10
    • 0242340484 scopus 로고    scopus 로고
    • On global solutions for the Constantin-Lax-Majda equation with a generalized viscosity term
    • Sakajo T. On global solutions for the Constantin-Lax-Majda equation with a generalized viscosity term. Nonlinearity 16 (2003) 1319-1328
    • (2003) Nonlinearity , vol.16 , pp. 1319-1328
    • Sakajo, T.1
  • 11
    • 84990556355 scopus 로고
    • Explicit solutions of the viscous model vorticity equation
    • Schochet S. Explicit solutions of the viscous model vorticity equation. Comm. Pure Appl. Math. 41 (1986) 531-537
    • (1986) Comm. Pure Appl. Math. , vol.41 , pp. 531-537
    • Schochet, S.1
  • 12
    • 0030577691 scopus 로고    scopus 로고
    • Behavior of solutions of model equations for incompressible fluid flow
    • Yang Y. Behavior of solutions of model equations for incompressible fluid flow. J. Differential Equations 125 (1996) 133-153
    • (1996) J. Differential Equations , vol.125 , pp. 133-153
    • Yang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.