Global Smooth Solutions for the Inviscid SQG Equation

In this paper, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.

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Hlavní autoři: Castro, Angel, Córdoba, Diego, Gómez-Serrano, Javier
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2020
Vydání:1
Edice:Memoirs of the American Mathematical Society
Témata:
Differential equations, Nonlinear
Differential equations, Nonlinear > Numerical solutions
Flows (Differentiable dynamical systems)
Fluid dynamics
Fluid dynamics > Mathematical models
Fluid mechanics
Geostrophic currents
Geostrophic currents > Mathematical models
Interval analysis (Mathematics)
Inviscid flow
Smoothness of functions
Global existence
surface quasi-geostrophic
incompressible
computer-assisted
ISBN:9781470442149, 1470442140
ISSN:0065-9266, 1947-6221
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Obsah:
  • Introduction -- The equations -- Main theorem and Crandall-Rabinowitz (C-R) theorem -- Checking the hypotheses of the C-R theorem for the equation 2.7 -- Asymptotics -- Implementation of the computer-assisted part and rigorous numerical results -- Finite projections
  • Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. The equations -- Chapter 3. Main theorem and Crandall-Rabinowitz (C-R) theorem -- Chapter 4. Checking the hypotheses of the C-R theorem for the equation 2.7 -- 4.1. Step 1. The functional setting and the hypothesis 1 -- 4.2. Step 2. The partial derivatives of the functional -- 4.3. Step 3. Analysis of the linear operator -- 4.4. Step 4. The transversality property 4 -- Acknowledgments -- Appendix A. Asymptotics -- Appendix B. Implementation of the computer-assisted part and rigorous numerical results -- Appendix C. Finite projections -- Bibliography -- Back Cover