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Exact self-similar finite-time blowup of the Hou-Luo model with smooth profiles

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arxiv 2308.01528 v3 pith:26E3MS7K submitted 2023-08-03 math.AP

De Huang , Xiang Qin , Xiuyuan Wang , Dongyi Wei This is my paper · ORCID
classification math.AP
keywords profilesself-similarblowupfinite-timehou-luomodelexactsmooth
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We show that the 1D Hou-Luo model on the real line admits exact self-similar finite-time blowup solutions with smooth self-similar profiles. The existence of these profiles is established via a fixed-point method that is purely analytic. We also prove that the profiles satisfy some monotonicity and convexity properties that were unknown before, and we give rigorous estimates on the algebraic decay rates of the profiles in the far field. Our result supplements the previous computer-assisted proof of self-similar finite-time blowup for the Hou-Luo model with finer characterizations of the profiles.

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  1. Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases

    math.AP 2025-01 conditional novelty 8.0 of 10

    For gamma = 5/3, corresponding to a monatomic gas, there exist smooth initial data for which the 3-D compressible Navier-Stokes equations blow up in finite time in a self-similar implosion.

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