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

DOI10.1016/j.aim.2006.07.021zbMath1133.35078OpenAlexW1969995390MaRDI QIDQ2642041

Pedro Balodis, Antonio Córdoba

Publication date: 20 August 2007

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2006.07.021

zbMATH Keywords

spherical harmonicstransport equationsRiesz transformsMellin multipliers

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

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Cites Work

• Integral inequalities for the Hilbert transform applied to a nonlocal transport equation
• Formation of singularities for a transport equation with nonlocal velocity
• Vorticity and Incompressible Flow
• Commutator estimates and the euler and navier-stokes equations
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