The Blow-up solutions for fractional heat equations on torus and Euclidean space

2019/11/03 by Divyang G. Bhimani, Bhimani, Divyang G.
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1911.01844

Abstract

We produce a finite time blow-up solution for nonlinear fractional heat equation (∂_t u + (-Δ)^β/2u=u^k) in modulation and Fourier amalgam spaces on the torus \mathbb T^d and the Euclidean space \mathbb R^d. This complements several known local and small data global well-posedness results in modulation spaces on \mathbb R^d. Our method of proof rely on the formal solution of the equation. This method should be further applied to other non-linear evolution equations.

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