Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces
Abstract
:1. Introduction
2. Momentum Formulation and Main Results
- If , then has two real eigenvalues:
- If , then has two complex conjugated eigenvalues:
3. The Global Well-Posedness
4. Gevrey Analyticity
5. The Asymptotic Behaviors
5.1. Uniform Upper Bounds on the Growth of Analyticity Radius
5.2. Optimal Time-Decay Rates
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Littlewood–Paley Theory and Besov Spaces
- If , , then
- If , , , then
- If , , then
Appendix B. Gevrey Estimates
- If , , then it holds for that
- If , , then it holds that
- If , , , then it holds thatMoreover, holds true for .
- If , , then it holds for thatwhere
- If , , then it also holds that
- If , , , then it also holds thatMoreover, holds true for .
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Song, Z.; Xu, J. Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces. Mathematics 2023, 11, 174. https://doi.org/10.3390/math11010174
Song Z, Xu J. Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces. Mathematics. 2023; 11(1):174. https://doi.org/10.3390/math11010174
Chicago/Turabian StyleSong, Zihao, and Jiang Xu. 2023. "Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces" Mathematics 11, no. 1: 174. https://doi.org/10.3390/math11010174
APA StyleSong, Z., & Xu, J. (2023). Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces. Mathematics, 11(1), 174. https://doi.org/10.3390/math11010174