%0 Journal Article
%T The Global Existence of Smooth Solutions for Timoshenko-Cattaneo System with Two-Sound Waves in Besov Space
%A Xin&#8217
%A ai Fu
%J Advances in Pure Mathematics
%P 235-246
%@ 2160-0384
%D 2025
%I Scientific Research Publishing
%R 10.4236/apm.2025.154011
%X 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 <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>s</mi><mo>=</mo><mfrac>
   <mn>3</mn>
   <mn>2</mn>
  </mfrac>
  </mrow>
</math>

.
%K Timoshenko-Cattaneo System
%K Regularity-Loss
%K Global Existence
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=141942