Author(s)

Xin’ai Fu

School of Mathematics and Key Laboratory of Mathematical MIIT, Nanjing University of Aeronautics and Astronautics, Nanjing, China.

This paper is devoted to studying the global existence of smooth solutions for the Timoshenko-Cattaneo system with two sound waves. In the case of equal wave speeds and non-equal wave speeds, the Timoshenko-Cattaneo system exhibits regularity loss in the high-frequency part in order to obtain global well-posedness for the nonlinear Timoshenko-Cattaneo system with the minimum initial value of regularity index. This article applied harmonic analysis tools to establish the global solution for the Timoshenko-Cattaneo system in Besov space with a regularity index $s=\frac{3}{2}$ .

Timoshenko-Cattaneo System, Regularity-Loss, Global Existence

Fu, X.A. (2025) The Global Existence of Smooth Solutions for Timoshenko-Cattaneo System with Two-Sound Waves in Besov Space. Advances in Pure Mathematics, 15, 235-246. doi: 10.4236/apm.2025.154011.