Blowup for projected 2-dimensional C2 solutions of compressible Euler equations with Coriolis force. (October 2020)

• Record Type: Journal Article
• Authors: Ho, Choryin; Yuen, Manwai
• Is Part Of: Nonlinear analysis. Volume 55(2020)
• Publication Date: 2020-10
• Subjects: Compressible Euler equations -- Coriolis force -- Blowup -- Initial value problem -- Functional method -- Non-vacuum; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103143
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Compressible Euler equations with Coriolis force are the fundamental model in the study of atmospheric dynamics. In this article, we study the lifespan of the projected 2-dimensional C 2 non-vacuum solutions of the compressible Euler equations with Coriolis force. We first locate the vortex equations for the compressible Euler equations with Coriolis force and then use the integration method to prove that the corresponding blowup results exist for the rotational C 2 solutions with a sufficiently large initial functional, H ( 0 ) = ∫ R 3 x → ⋅ u → 0 d V . Based on these new results for the system, the presence of Coriolis forces makes the inflation conditions more difficult to be satisfied.