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Reviewed by Hidetoshi Tahara References

By Dong (-iasp-sm) Rodrigo and José Luis (-warw-mr

Abstract

Blow-up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation. (English summary) Adv. Math. 217 (2008), no. 6, 2563–2568. The paper considers a 1D transport equation with nonlocal velocity and supercritical dissipation of the form (1) θt + (Hθ)θx = −κΛ γ θ, t> 0, x ∈ R, where Hθ is the Hilbert transform defined by Hθ = 1 π P.V. θ(y) x − y dy, κ is a positive number, Λ γ θ = (−∆) γ/2 θ and 0 ≤ γ < 1/2. The main result is as follows: For a certain class of initial data the solutions of (1) blow up in finite time

Topics: 8. H. Dong, Well-posedness for a transport equation with nonlocal velocity, preprint. cf. MR
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.353.2279
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