Collected Papers in Honor of Yoshihiro Shibata / / edited by Tohru Ozawa

• Record Nr.: UNINA9910633925403321
• Pubbl/distr/stampa: Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2022
• ISBN: 9783031192524; 9783031192517
• Edizione: [1st ed. 2022.]
• Descrizione fisica: 1 online resource (396 pages)
• Collana: Mathematics and Statistics Series
• Disciplina: 531; 532.00151
• Soggetti: Differential equations; Continuum mechanics; Differential Equations; Continuum Mechanics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Contents -- Preface -- References -- Global Wellposedness of the Primitive Equations with Nonlinear Equation of State in Critical Spaces -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Typical Ocean Densities -- 3.1. Linear Density -- 3.2. Equation of State by TEOS-10 -- 3.3. Equation of State by McDongall-Jacket-Wright-Feistel -- 3.4. Equation of State by UNESCO-80 -- 4. Main Result -- 5. Estimates for the Local Existence -- 6. A Priori Estimates -- 7. Proof of Theorem 4.1 -- 7.1. Local Wellposedness -- 7.2. Global Wellposedness -- Appendix A. Semilinear Evolution Equations and Maximal Lr-Regularity -- References -- On the Global Existence for the Compressible Euler-Riesz System -- Abstract -- Introduction -- 1. Main Results -- 2. A Local in Time Result for Non-decaying Data -- 2.1. A Priori Estimates -- 2.2. About the Proof of Existence -- 2.3. Uniqueness -- 3. A Global Existence Result -- 3.1. A Priori Estimates -- 3.2. Existence -- 3.3. The Proof of Uniqueness -- 3.4. Instability of Nontrivial Static Solutions in the Attractive Case -- 4. About Ideal Gases -- 4.1. Local Existence -- 4.2. Global Existence -- 4.3. Remark on Static Solutions -- Appendix -- Acknowledgements -- References -- ; Rotation Problem for a Two-Phase Drop -- Abstract -- 1. Introduction -- 2. Linear Problem -- 3. The Nonlinear Problem -- References -- On the Stokes-Type Resolvent Problem Associated with Time-Periodic Flow Around a Rotating Obstacle -- Abstract -- 1. Introduction -- 2. Notation -- 3. Main Results -- 4. The Resolvent Problem in the Whole Space -- 5. The Resolvent Problem in an Exterior Domain -- 6. The Time-Periodic Problem -- References -- Euler System with a Polytropic Equation of State as a Vanishing Viscosity Limit -- Abstract -- 1. Introduction -- 2. Preliminary Material -- 2.1. Mathematical Theory of the Closed System.; 2.2. Transport Coefficients -- 2.3. Equation of State -- 2.4. Relative Energy -- 3. Main Results -- 3.1. Unconditional Convergence in the Absence of Boundary Layer -- 3.2. Conditional Result: Viscous Boundary Layer -- 4. Consistency of the Vanishing Dissipation/Radiation Approximation -- 4.1. Temperature for the Euler System -- 4.2. Consistency -- 4.2.1. Viscous Stress Consistency -- 4.2.2. Heat Flux Consistency -- 4.2.3. Radiation Entropy Convective Flux Consistency -- 5. Convergence -- 5.1. Velocity Regularization -- 5.2. Application of the Relative Energy Inequality -- 5.3. Integrals Controlled by the Consistency Estimates -- 5.4. Integrals Independent of the Boundary Layer -- 5.5. Boundary Layer -- 5.5.1. Viscous Stress -- 5.5.2. Convective Term -- 5.6. Strong Convergence -- References -- On the Hydrostatic Approximation of Compressible Anisotropic Navier-Stokes Equations-Rigorous Justification -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Main Result -- 3.1. Dissipative Weak Solutions of CNS -- 3.2. Strong Solution of CPE -- 3.3. Versatile Relative Entropy Inequality -- 3.4. Main Result -- 4. Convergence -- 4.1. Main Idea of Proof -- 4.2. Step 1 -- 4.3. Step 2 -- 4.4. Step 3 -- Acknowledgements -- References -- A Route to Chaos in Rayleigh-Bénard Heat Convection -- Abstract -- 1. Introduction -- 2. linear Stability and Critical Rayleigh Number -- 3. Routes to Chaos -- 3.1. Roll Solutions on Bifurcation Branches in the Large -- 3.2. Time Evolution of Roll Solutions and the Secondary Hopf Bifurcation -- 3.3. Concluding Remark -- Acknowledgements -- References -- Existence of Weak Solution to the Nonstationary Navier-Stokes Equations Approximated by Pressure Stabilization Method -- Abstract -- 1. Introduction -- 2. Notations and Main Results -- 3. Preliminaries -- 4. Proof of Main Results -- Acknowledgements -- References.; Resolvent Estimates for a Compressible Fluid Model of Korteweg Type and Their Application -- Abstract -- 1. Introduction -- 2. Notation and Main Results -- 2.1. Notation -- 2.2. Main Results -- 3. Preliminaries -- 3.1. Some Inequalities -- 3.2. Compact Embeddings -- 3.3. Results of the Large Resolvent Parameter -- 3.4. Maximal Regularity -- 4. The Problem in Bounded Domains -- 4.1. Existence of Solutions -- 4.2. Uniqueness of Solutions -- 4.3. A Priori Estimates -- 4.4. Proof of Theorem 2.5 -- 4.5. Proof of Theorem 2.6 -- 5. The Whole Space Problem -- 5.1. Representation Formulas of Solutions -- 5.2. Estimates of P(ξ,λ) for γ=0. -- 5.3. Estimates of P(ξ,λ) for γ&gt -- 0. -- 5.4. Proof of Theorem 5.1 -- 6. The Problem in Exterior Domains -- 6.1. Construction of Parametrix -- 6.2. Uniqueness of Solutions -- 6.3. A Priori Estimates -- 6.4. An Auxiliary Problem -- 6.5. Proof of Theorem 2.1 -- 7. Application to a Nonlinear Problem -- 7.1. Generation of an Analytic C0-Semigroup -- 7.2. Maximal Regularity with Exponential Stability -- 7.3. Estimates of Nonlinear Terms -- 7.4. Global Solvability of the Nonlinear Problem -- References -- Rate of the Enhanced Dissipation for the Two-jet Kolmogorov Type Flow on the Unit Sphere -- Abstract -- 1. Introduction -- 2. Preliminaries -- 3. Analysis of the Linearized Operator -- 3.1. Settings and Basic Results -- 3.2. ; Verification of Assumption 4.6 -- 3.3. Estimates for the Semigroup -- 4. Abstract Results -- 5. Appendix: Basic Formulas of Differential Geometry -- Acknowledgements -- References -- Reacting Multi-component Fluids: Regular Solutions in Lorentz Spaces -- Abstract -- 1. Introduction -- 2. Functional Spaces and the Main Result -- 3. Auxiliary Results and Linear Theory -- 4. A Priori Estimates -- 4.1. Velocity Bounds -- 4.2. Estimates for the Density -- 5. Existence -- Acknowledgements -- References.; Global Well Posedness for a Q-tensor Model of Nematic Liquid Crystals -- Abstract -- 1. Introduction -- 2. Maximal Lp-Lq Regularity -- 2.1. mathcalR-boundedness of Solution Operators -- 2.2. A Proof of Theorem 2.1 -- 3. Decay Property of Solutions to the Linearized Problem -- 3.1. Decay Estimates for d -- 3.2. Decay Estimates for U and mathbbQ -- 3.2.1. Analysis of Low Frequency Parts -- 3.2.2. Analysis of High Frequency Parts -- 4. A Proof of Theorem 1.1 -- 4.1. Analysis of Time Shifted Equations -- 4.2. Analysis of Compensation Equations -- 4.2.1. Estimates of Spatial Derivatives in Lp-Lq -- 4.2.2. Estimates of Time Derivatives in Lp-Lq -- 4.2.3. Estimates of the Lower Order Term in Linfty-Lq -- 4.3. Conclusion -- References -- Maximal Regularity for Compressible Two-Fluid System -- Abstract -- 1. Introduction -- 1.1. Notation -- 1.2. Main Results -- 1.3. Discussion -- 2. Lagrangian Coordinates -- 3. Local Well-Posedness -- 3.1. Linearization Around the Initial Condition -- 3.2. Maximal Regularity -- 3.3. Preliminary Estimates -- 3.4. Estimate of the Right Hand Side of (3.3) -- 3.5. Contraction Argument-Proof of Theorem 1.1 -- 4. Global Well-Posedness -- 4.1. Linearization Around the Constant State -- 4.2. Exponential Decay -- 4.3. Bounds for Nonlinearities -- 4.4. Proof of Theorem 1.2 -- Appendix -- Acknowledgements -- References -- Steady Compressible Navier-Stokes-Fourier Equations with Dirichlet Boundary Condition for the Temperature -- Abstract -- 1. Introduction -- 2. Formulation of the Problem: Main Result -- 3. Weak Compactness of Weak and Variational Entropy Ballistic Solutions -- 3.1. A Priori Estimates -- 3.2. Weak Compactness -- 4. Construction of the Solution -- References -- A Slightly Supercritical Condition of Regularity of Axisymmetric Solutions to the Navier-Stokes Equations -- Abstract -- 1. Introduction -- 2. Auxiliary Facts.; 3. Proof of Proposition 1.4 -- 4. Proof of Theorem 1.3 -- Acknowledgements -- References -- Spatial Pointwise Behavior of Time-Periodic Navier-Stokes Flow Induced by Oscillation of a Moving Obstacle -- Abstract -- 1. Introduction -- 2. Results -- 2.1. Notation -- 2.2. Evolution Operator -- 2.3. Main Results -- 3. Proof of Theorem 2.1 -- 3.1. Weak Form of the Integral Equation -- 3.2. Regularity in x -- 3.3. Regularity in t and the Pressure -- 4. Proof of Theorem 2.2 -- 4.1. Reduction to the Whole Space Problem -- 4.2. Integral Equation for the Whole Space Problem -- 4.3. Reconstruction Procedure -- References.
• Sommario/riassunto: Yoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations. The papers collected here — on the occasion of his 70th birthday — are written by world-renowned researchers and celebrate his decades of outstanding achievements.