Global well-posedness and symmetries for dissipative active scalar equations with positive-order couplings

• Autores: Lucas C. F. Ferreira, Lidiane S. M. Lima
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 60, Nº 2, 2016, págs. 525-550
• Idioma: inglés
• DOI: 10.5565/10.5565-PUBLMAT_60216_08
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• Resumen

  • We consider a family of dissipative active scalar equations outside the L2-space. This was introduced in [7] and its velocity fields are coupled with the active scalar via a class of multiplier operators which morally behave as derivatives of positive order. We prove global well-posedness and time-decay of solutions, with-out smallness assumptions, for initial data belonging to the critical Lebesgue space Ln/2y-β (ℝn ) which is a class larger than that of the above reference. Symmetry properties of solutions are investigated depending on the symmetry of initial data and coupling operators.