% ============================================================================= % BibTeX Bibliography for: % "Global Regularity of the 3D Incompressible Navier-Stokes Equations % on a Discrete Bounded Lattice" % Author: Rafael D. De Paz % ============================================================================= % --- Core Navier-Stokes Literature --- @article{Leray1934, author = {Leray, Jean}, title = {Sur le mouvement d'un liquide visqueux emplissant l'espace}, journal = {Acta Mathematica}, volume = {63}, pages = {193--248}, year = {1934}, doi = {10.1007/BF02547354} } @article{CKN1982, author = {Caffarelli, Luis and Kohn, Robert and Nirenberg, Louis}, title = {Partial regularity of suitable weak solutions of the {N}avier-{S}tokes equations}, journal = {Communications on Pure and Applied Mathematics}, volume = {35}, number = {6}, pages = {771--831}, year = {1982}, doi = {10.1002/cpa.3160350604} } @article{Tao2016, author = {Tao, Terence}, title = {Finite time blowup for an averaged three-dimensional {N}avier-{S}tokes equation}, journal = {Journal of the American Mathematical Society}, volume = {29}, number = {3}, pages = {601--674}, year = {2016}, doi = {10.1090/jams/838} } @book{Temam2001, author = {Temam, Roger}, title = {Navier-{S}tokes Equations: Theory and Numerical Analysis}, publisher = {American Mathematical Society}, year = {2001}, edition = {Reprint}, isbn = {978-0-8218-2737-6} } @book{Lions1969, author = {Lions, Jacques-Louis}, title = {Quelques méthodes de résolution des problèmes aux limites non linéaires}, publisher = {Dunod}, year = {1969} } @article{ConstantinFoias1988, author = {Constantin, Peter and Foias, Ciprian}, title = {Navier-{S}tokes Equations}, publisher = {University of Chicago Press}, year = {1988}, journal = {Chicago Lectures in Mathematics} } @article{Hopf1951, author = {Hopf, Eberhard}, title = {\"Uber die {A}nfangswertaufgabe f\"ur die hydrodynamischen {G}rundgleichungen}, journal = {Mathematische Nachrichten}, volume = {4}, pages = {213--231}, year = {1951}, doi = {10.1002/mana.3210040121} } @article{LadyzhenskayaSerrin1967, author = {Serrin, James}, title = {On the interior regularity of weak solutions of the {N}avier-{S}tokes equations}, journal = {Archive for Rational Mechanics and Analysis}, volume = {9}, pages = {187--195}, year = {1962}, doi = {10.1007/BF00253344} } @book{Ladyzhenskaya1969, author = {Ladyzhenskaya, Olga A.}, title = {The Mathematical Theory of Viscous Incompressible Flow}, publisher = {Gordon and Breach}, year = {1969}, edition = {2nd} } % --- Discrete / Lattice Methods --- @article{ChorinMarsden1993, author = {Chorin, Alexandre Joel and Marsden, Jerrold E.}, title = {A Mathematical Introduction to Fluid Mechanics}, publisher = {Springer}, year = {1993}, edition = {3rd}, journal = {Texts in Applied Mathematics} } @article{Succi2001, author = {Succi, Sauro}, title = {The Lattice {B}oltzmann Equation for Fluid Dynamics and Beyond}, publisher = {Oxford University Press}, year = {2001}, journal = {Numerical Mathematics and Scientific Computation} } @article{JunkYang2005, author = {Junk, Michael and Yang, Zhaoxia}, title = {Asymptotic analysis of lattice {B}oltzmann boundary conditions}, journal = {Journal of Statistical Physics}, volume = {121}, pages = {3--35}, year = {2005}, doi = {10.1007/s10955-005-8321-2} } @article{GoldsteinHardyPomeranceTaylor1993, author = {Hardy, J. and Pomeau, Y. and de Pazzis, O.}, title = {Time evolution of a two-dimensional model system. {I}. {I}nvariant states and time correlation functions}, journal = {Journal of Mathematical Physics}, volume = {14}, number = {12}, pages = {1746--1759}, year = {1973}, doi = {10.1063/1.1666248} } % --- Discrete Calculus and Numerical Analysis --- @book{LeVeque2007, author = {LeVeque, Randall J.}, title = {Finite Difference Methods for Ordinary and Partial Differential Equations}, publisher = {SIAM}, year = {2007}, isbn = {978-0-898716-29-0} } @article{Lax1954, author = {Lax, Peter and Richtmyer, Robert D.}, title = {Survey of the stability of linear finite difference equations}, journal = {Communications on Pure and Applied Mathematics}, volume = {9}, pages = {267--293}, year = {1956}, doi = {10.1002/cpa.3160090206} } @article{CFL1928, author = {Courant, Richard and Friedrichs, Kurt and Lewy, Hans}, title = {\"Uber die partiellen {D}ifferenzengleichungen der mathematischen {P}hysik}, journal = {Mathematische Annalen}, volume = {100}, pages = {32--74}, year = {1928}, doi = {10.1007/BF01448839} } % --- Physical Discreteness / Planck Scale --- @article{Planck1899, author = {Planck, Max}, title = {\"Uber irreversible {S}trahlungsvorga\"nge}, journal = {Sitzungsberichte der K\"oniglich Preu\ss{}ischen Akademie der Wissenschaften zu Berlin}, year = {1899}, pages = {440--480} } @article{Rovelli2004, author = {Rovelli, Carlo}, title = {Quantum Gravity}, publisher = {Cambridge University Press}, year = {2004}, journal = {Cambridge Monographs on Mathematical Physics} } @article{tHooft1993, author = {'t Hooft, Gerard}, title = {Dimensional reduction in quantum gravity}, journal = {arXiv preprint gr-qc/9310026}, year = {1993} } % --- Functional Analysis --- @book{Evans2010, author = {Evans, Lawrence C.}, title = {Partial Differential Equations}, publisher = {American Mathematical Society}, year = {2010}, edition = {2nd}, series = {Graduate Studies in Mathematics}, volume = {19} } @book{Robinson2001, author = {Robinson, James C.}, title = {Infinite-Dimensional Dynamical Systems}, publisher = {Cambridge University Press}, year = {2001} } % --- Clay Mathematics Institute --- @misc{ClayNS, author = {{Clay Mathematics Institute}}, title = {Navier-{S}tokes Existence and Smoothness}, year = {2000}, url = {https://www.claymath.org/millennium/navier-stokes-equation/}, note = {Millennium Prize Problem, official problem statement by C.~L.~Fefferman} } @article{Fefferman2006, author = {Fefferman, Charles L.}, title = {Existence and Smoothness of the {N}avier-{S}tokes Equation}, journal = {Clay Mathematics Institute Millennium Prize Problems}, year = {2000}, pages = {57--67}, url = {https://www.claymath.org/millennium/navier-stokes-equation/} } % --- Energy Methods and Gronwall --- @article{Gronwall1919, author = {Gronwall, Thomas H.}, title = {Note on the derivatives with respect to a parameter of the solutions of a system of differential equations}, journal = {Annals of Mathematics}, volume = {20}, number = {4}, pages = {292--296}, year = {1919}, doi = {10.2307/1967124} } @article{Navier1822, author = {Navier, Claude-Louis}, title = {M\'emoire sur les lois du mouvement des fluides}, journal = {M\'emoires de l'Acad\'emie Royale des Sciences de l'Institut de France}, volume = {6}, pages = {389--440}, year = {1822} } @article{Stokes1845, author = {Stokes, George Gabriel}, title = {On the theories of the internal friction of fluids in motion}, journal = {Transactions of the Cambridge Philosophical Society}, volume = {8}, pages = {287--319}, year = {1845} } @article{leray1822mouvement, title={Sur le mouvement d'un liquide visqueux emplissant l'espace}, author={Leray, Jean}, journal={Acta Mathematica}, volume={63}, pages={193--248}, year={1934}, publisher={Springer} } @book{temam2001navier, title={Navier-Stokes equations: theory and numerical analysis}, author={Temam, Roger}, year={2001}, publisher={American Mathematical Soc.} }