Formation of singularities for a transport equation with nonlocal velocity

• Autores: Diego Córdoba Gazolaz, Marco Antonio Fontelos, Antonio Córdoba Barba
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 162, Nº 3, 2005, págs. 1375-1387
• Idioma: inglés
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• Resumen

  • We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist globally in time.