Blow-up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation

74 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On a transport equation with nonlocal drift (2014, methodology): “In order to treat the nonlocal term, we appeal to a trick already present in [28,32], namely that Λ α (Λ γ θ )( t, 0) = Λ α + γ θ ( t, 0).”
Finite-Time Singularities of an Aggregation Equation in $${\mathbb {R}^n}$$ with Fractional Dissipation (2009, methodology): “We refer the reader to [10],[9] and [27] where this type of dissipation has been used in the context of the surface quasi-geostrophic equation and other one dimensional models, for a more detailed explanation of the 3 regimes.”
Exploding solutions for a nonlocal quadratic evolution problem (2010, background): “We refer the interested reader to [1, 12, 15, 16, 17, 18, 19, 21] where other equations with fractal type diffusion have been considered.”