Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows
Abstract
:1. Introduction
2. Lagrangian Formulation
3. Estimates of Nonlinear Terms
3.1. Estimates of
3.2. Estimates of
3.3. Estimates of
4. A Priori Estimates for Linearized Problems
4.1. Estimates of
4.1.1. Analysis of Time Shifted Equations
4.1.2. Analysis of Compensation Equations for
4.1.3. Analysis of Compensation Equations for k
4.2. Estimates of
5. A Proof of Theorem 2
6. Proof of Theorem 1
7. Concluding Remarks
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Murata, M. Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows. Mathematics 2023, 11, 181. https://doi.org/10.3390/math11010181
Murata M. Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows. Mathematics. 2023; 11(1):181. https://doi.org/10.3390/math11010181
Chicago/Turabian StyleMurata, Miho. 2023. "Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows" Mathematics 11, no. 1: 181. https://doi.org/10.3390/math11010181
APA StyleMurata, M. (2023). Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows. Mathematics, 11(1), 181. https://doi.org/10.3390/math11010181