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Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik
An essential companion to M. Vishik’s groundbreaking work in fluid mechanics The incompressible Euler equations are a system of partial differential equations introduced by Leonhard Euler more than 250 years ago to describe the motion of an inviscid incompressible fluid. These equations can be derived from the classical conservations laws of mass and momentum under some very idealized assumptions. While they look simple compared to many other equations of mathematical physics, several fundamental mathematical questions about them are still unanswered. One is under which assumptions it can be rigorously proved that they determine the evolution of the fluid once we know its initial state and the forces acting on it. This book addresses a well-known case of this question in two space dimensions. Following the pioneering ideas of M. Vishik, the authors explain in detail the optimality of a celebrated theorem of V. Yudovich from the 1960s, which states that, in the vorticity formulation, the solution is unique if the initial vorticity and the acting force are bounded. In particular, the authors show that Yudovich’s theorem cannot be generalized to the L^p setting.
The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations
The aim of this book is to provide beginning graduate students who completed the first two semesters of graduate-level analysis and PDE courses with a first exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces. Chapters 1 and 2 cover the fundamentals of the Euler theory: derivation, Eulerian and Lagrangian perspectives, vorticity, special solutions, existence theory for smooth solutions, and blowup criteria. Chapters 3, 4, and 5 cover ...
Adventures of a Foot Washer
Cynicism is strong in the newspaper business where I have worked for more than 30 years. But Carlos Alonso is a bright spot in my career. A respected missionary, he is committed to serving Jesus Christ in every aspect of his life. One of my articles was about Carlos taking the Gospel to his family in Cuba after 20 years in the United States. He led them all to the Lord, which is typical of the fruit God has born through his obedience. Boldness is a strong attribute in Carlos. He does not hold back when the Lord speaks to Him. As missionary and prophet he travels the world preaching Jesus, laying hands on the sick and setting captives free through the power of the Holy Spirit. In Adventures of a Foot Washer, he tells of many encounters with the power Jesus and the miracles he has witnessed. He shares his story with humility, yet with a confidence that comes from obedience to God. Take this journey with Carlos and see how the Holy Spirit can touch you as a believer. As a Christian for more than 35 years, I assure you that it will be a trip worth taking. Michelle Jones Journalist
Adaptive Control of Parabolic PDEs
This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book also presents a rich collection of methods for system identification of PDEs, methods that employ Lyapunov, passivity, observer-based, swapping-based, gradient, and least-squares tools and parameterizations, among others. Including a wealth of stimulating ideas and providing the mathematical and control-systems background needed to follow the designs and proofs, the book will be of great use to students and researchers in mathematics, engineering, and physics. It also makes a valuable supplemental text for graduate courses on distributed parameter systems and adaptive control.
The Florida Bar Journal
Proceedings of the 21st-43d annual convention of the Florida State Bar Association included in v. 2-24; lst- annual convention of the Florida Bar in v.24-
Limpy
limpy is a gripping story about men of faith (limpy, Mishpat and Didasko) who are mortified to discover that, even in the church they love, the ways of the Bible have been corrupted exactly as foretold by Jesus 2,000 years before. They suffer as they realize that cherished practices are not only wrong, but cannot possibly meet the needs of God's children. This anguishing discovery compels them to actions they could not have imagined. Their answer to the plague of today's church-which makes limpy a must read book-is wonderfully enriched by the nobility of their lives as the tale unfolds. But there is more. Truth that is greater than life emerges from deep within the pathos of their struggle. A groan uttered by creation itself travails for the manifesting of the sons of God. There is an unquenchable thirsting, an insatiable hungering for His fullness; a groaning to be home with Him, forever. When you read limpy, you will know it is so; and you will be comforted. The book is both promise and warning. In the fullness of time, God will gather believing Jews and Gentiles to be a holy temple, a dwelling place for Himself in the Spirit.
Z każdym twoim oddechem. Amerykański True Crime
„Jeśli kiedykolwiek coś mi się stanie... znajdź Ann Rule i poproś ją o napisanie mojej historii”. W prawdopodobnie pierwszej książce z gatunku true crime napisanej na prośbę ofiary, Ann Rule rozplątuje pełną brutalności sieć kłamstw, której kulminacją było morderstwo Sheili Blackthorne Bellush – kobiety, której Rule nigdy nie spotkała, ale której szokującą historię opisuje z niebywałą dokładnością, ale również ze współczuciem. Mimo że ma nową rodzinę, Sheila nigdy tak naprawdę nie uwolniła się od swojego byłego męża, multimilionera Allena Blackthorne'a, z pozoru przystojnego i czarującego, a w rzeczywistości brutalnego, posiadającego potrzebę kontroli socjopaty, który terroryzował Sheilę nie tylko w małżeństwie, ale jeszcze dekadę po rozwodzie. Kiedy Sheila została zamordowana we własnym domu, w obecności czwórki swoich małych dzieci, władze zaczęły łączyć zbrodnię z Blackthorne'em – mężczyzną, który w swoim obsesyjnym dążeniu do władzy i zemsty poprzysiągł monitorować każdy ruch Sheili.
