An inequality for Riesz transforms implying blow-up for some nonlinear and nonlocal transport equations

• Autores: Pedro Balodis Matesanz, Antonio Córdoba Barba
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 214, Nº 1, 2007, págs. 1-39
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.07.021
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• Resumen

  • A proof of a new integral inequality for the Riesz transforms is presented, together with applications to obtain blow-up, in finite time, for a general class of initial data on a nonlinear transport equation having a nonlocal velocity field given by the Riesz transforms of the active scalar.