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Global well-posedness for Euler-Boussinesq system with critical dissipation. (English) Zbl 1284.76089

Summary: We study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] DOI: 10.1137/070682319 · Zbl 1157.76054 · doi:10.1137/070682319
[2] DOI: 10.1007/BF01212349 · Zbl 0573.76029 · doi:10.1007/BF01212349
[3] DOI: 10.1016/j.anihpc.2004.10.010 · Zbl 1157.35469 · doi:10.1016/j.anihpc.2004.10.010
[4] Bony J.-M., Ann. de l’Ecole Norm. Sup. 14 pp 209– (1981)
[5] DOI: 10.1007/s00332-009-9044-3 · Zbl 1177.49064 · doi:10.1007/s00332-009-9044-3
[6] DOI: 10.1016/j.aim.2005.05.001 · Zbl 1100.35084 · doi:10.1016/j.aim.2005.05.001
[7] Chemin J.-Y., Perfect Incompressible Fluids (1998)
[8] DOI: 10.1007/s00220-007-0193-7 · Zbl 1142.35069 · doi:10.1007/s00220-007-0193-7
[9] Constantin P., Indiana Univ. Math. J. 50 pp 97– (2001)
[10] DOI: 10.1088/0951-7715/7/6/001 · Zbl 0809.35057 · doi:10.1088/0951-7715/7/6/001
[11] DOI: 10.1137/S0036141098337333 · Zbl 0957.76093 · doi:10.1137/S0036141098337333
[12] DOI: 10.1007/s00220-004-1055-1 · Zbl 1309.76026 · doi:10.1007/s00220-004-1055-1
[13] DOI: 10.1007/s00220-009-0821-5 · Zbl 1186.35157 · doi:10.1007/s00220-009-0821-5
[14] DOI: 10.1007/s00205-008-0115-7 · Zbl 1147.76014 · doi:10.1007/s00205-008-0115-7
[15] DOI: 10.1512/iumj.2009.58.3590 · Zbl 1178.35303 · doi:10.1512/iumj.2009.58.3590
[16] DOI: 10.1016/j.jde.2010.07.008 · Zbl 1200.35228 · doi:10.1016/j.jde.2010.07.008
[17] Hou T.Y., Discr. Cont. Dyn. Sys. 12 pp 1– (2005)
[18] DOI: 10.1007/s00222-006-0020-3 · Zbl 1121.35115 · doi:10.1007/s00222-006-0020-3
[19] Stein E.M., Singular Integrals and Differentiability Properties of Functions (1970) · Zbl 0207.13501
[20] DOI: 10.1007/s002050050128 · Zbl 0926.35123 · doi:10.1007/s002050050128
[21] DOI: 10.1063/1.868044 · Zbl 0822.76087 · doi:10.1063/1.868044
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