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On the spectrum of Euler-Lagrange operator in the stability analysis of Benard problem
  • JIe Wang,
  • LANXI XU
JIe Wang
Beijing University of Chemical Technology

Corresponding Author:1578807189@qq.com

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LANXI XU
Beijing University of Chemical Technology
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Abstract

In studying the stability of B\’{e}nard problem we usually have to solve a variational problem to determine the critical Rayleigh number for linear or nonlinear stability. To solve the variational problem one usually transform it to an eigenvalue problem which is called Euler-Lagrange equations. An operator related to the Euler-Lagrange equations is usually referred to as Euler-Lagrange operator whose spectrum is investigated in this paper. We have shown that the operator possesses only the point spectrum consisting of real number, which forms a countable set. Moreover, it is found that the spectrum of the Euler-Lagrange operator depends on the thickness of the fluid layer.
20 Apr 2022Submitted to Mathematical Methods in the Applied Sciences
21 Apr 2022Submission Checks Completed
21 Apr 2022Assigned to Editor
26 Apr 2022Reviewer(s) Assigned
21 Jun 2022Review(s) Completed, Editorial Evaluation Pending
22 Jun 2022Editorial Decision: Revise Minor
25 Jun 20221st Revision Received
27 Jun 2022Submission Checks Completed
27 Jun 2022Assigned to Editor
28 Jun 2022Review(s) Completed, Editorial Evaluation Pending
28 Jun 2022Editorial Decision: Accept