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Volumn 58, Issue 2, 2009, Pages 807-821

Finite time singularities and global well-posedness for fractal Burgers equations

Author keywords

Burgers equation; Finite time singularaties; Global well posedness; spatial analyticity

Indexed keywords


EID: 67249097393     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2009.58.3505     Document Type: Article
Times cited : (81)

References (16)
  • 1
    • 34447257464 scopus 로고    scopus 로고
    • N. ALIBAUD, J. DRONIOU, and J. VOVELLE, Occurrence and non-appearance of shocks in fractal Burgers equations, J. Hyperbolic Differ. Equ. 4 (2007), 479-499, http://dx.doi.org/10.1142/ S0219891607001227. MR 2339805 (2008i:35198)
    • N. ALIBAUD, J. DRONIOU, and J. VOVELLE, Occurrence and non-appearance of shocks in fractal Burgers equations, J. Hyperbolic Differ. Equ. 4 (2007), 479-499, http://dx.doi.org/10.1142/ S0219891607001227. MR 2339805 (2008i:35198)
  • 2
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • 85j:35154
    • J. T. BEALE, T. KATO, and A. MAJDA, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Comm. Math. Phys. 94 (1984), 61-66, http://dx.doi.org/10.1007/BF01212349. MR 763762 (85j:35154)
    • (1984) Comm. Math. Phys , vol.94 , pp. 61-66
    • BEALE, J.T.1    KATO, T.2    MAJDA, A.3
  • 3
    • 0002015456 scopus 로고    scopus 로고
    • Fractal Burgers equations, J
    • MR 1637513 99g:35111
    • P. BILER, T. FUNAKI, and W. A. WOYCZYNSKI, Fractal Burgers equations, J. Differential Equa-tions 148 (1998), 9-46, http://dx.doi.org/10.1006/jdeq.1998.3458. MR 1637513 (99g:35111)
    • (1998) Differential Equa-tions , vol.148 , pp. 9-46
    • BILER, P.1    FUNAKI, T.2    WOYCZYNSKI, W.A.3
  • 4
    • 84990556249 scopus 로고
    • A simple one-dimensional model for the three-dimensional vorticity equation
    • 87a:76037
    • P. CONSTANTIN, P. D. LAX, and A. MAJDA, A simple one-dimensional model for the three-dimensional vorticity equation, Comm. Pure Appl. Math. 38 (1985), 715-724, http://dx.doi.org/10.1002/cpa. 3160380605. MR 812343 (87a:76037)
    • (1985) Comm. Pure Appl. Math , vol.38 , pp. 715-724
    • CONSTANTIN, P.1    LAX, P.D.2    MAJDA, A.3
  • 5
    • 0043172071 scopus 로고
    • Formation of strong fronts in the 2-D quasi-geostrophic thermal active scalar
    • 95i:76107
    • P. CONSTANTIN, A. J. MAJDA, and E. TABAK, Formation of strong fronts in the 2-D quasi-geostrophic thermal active scalar, Nonlinearity 7 (1994), 1495-1533, http://dx.doi.org/10.1088/0951- 7715/7/6/001. MR 1304437 (95i:76107)
    • (1994) Nonlinearity , vol.7 , pp. 1495-1533
    • CONSTANTIN, P.1    MAJDA, A.J.2    TABAK, E.3
  • 6
    • 33745899606 scopus 로고    scopus 로고
    • A. CóRDOBA, D. CóRDOBA, and M. A. FONTELOS, Formation of singularities for a trans-port equation with nonlocal velocity, Ann. of Math. (2) 162 (2005), 1377-1389. MR 2179734 (2007b:35011)
    • A. CóRDOBA, D. CóRDOBA, and M. A. FONTELOS, Formation of singularities for a trans-port equation with nonlocal velocity, Ann. of Math. (2) 162 (2005), 1377-1389. MR 2179734 (2007b:35011)
  • 7
    • 33751328809 scopus 로고    scopus 로고
    • -, Integral inequalities for the Hilbert transform applied to a nonlocal transport equation, J. Math. Pures Appl. (9) 86 (2006), 529-540. MR 2281451 (2007k:35040) (English, with English and French summaries)
    • -, Integral inequalities for the Hilbert transform applied to a nonlocal transport equation, J. Math. Pures Appl. (9) 86 (2006), 529-540. MR 2281451 (2007k:35040) (English, with English and French summaries)
  • 9
    • 54949113612 scopus 로고    scopus 로고
    • Well-posedness for a transport equation with nonlocal velocity
    • MR 2464570
    • -, Well-posedness for a transport equation with nonlocal velocity, J. Funct. Anal. 255 (2008), 3070-3097. MR 2464570
    • (2008) J. Funct. Anal , vol.255 , pp. 3070-3097
    • DONG, H.1
  • 10
    • 50249090960 scopus 로고    scopus 로고
    • H. DONG and D. DU, Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space, Discrete Contin. Dyn. Syst. 21 (2008), 1095-1101, http://dx.doi.org/10.3934/dcds.2009.23.765. MR 2399451 (2009b:76175)
    • H. DONG and D. DU, Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space, Discrete Contin. Dyn. Syst. 21 (2008), 1095-1101, http://dx.doi.org/10.3934/dcds.2009.23.765. MR 2399451 (2009b:76175)
  • 12
    • 54949154201 scopus 로고    scopus 로고
    • -, Finite time singularities for a class of generalized surface quasi-geostrophic equations, Proc. Amer. Math. Soc. 136 (2008), 2555-2563, http://dx.doi.org/10.1090/S0002-9939-08-09328-3. MR 2390526 (2009c:35361)
    • -, Finite time singularities for a class of generalized surface quasi-geostrophic equations, Proc. Amer. Math. Soc. 136 (2008), 2555-2563, http://dx.doi.org/10.1090/S0002-9939-08-09328-3. MR 2390526 (2009c:35361)
  • 13
    • 64549139774 scopus 로고    scopus 로고
    • Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations
    • -, Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations, Comm. Math. Sci. 7 (2009), 67-80.
    • (2009) Comm. Math. Sci , vol.7 , pp. 67-80
    • DONG, H.1    LI, D.2


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