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The articles in this book encompass a broad historical panorama and consider the presence of litanic prayers and songs in different religions, beginning with written records in the Egyptian, Sumerian and Hebrew languages and finishing with Christian works from diverse denominations. The research presents the litany as an exceptionally long-lasting genre which for several thousand years existed in the Middle-Eastern and European traditions, easily conforming to changes in religious or historical circumstances. An interdisciplinary approach by scholars representing different fields of study, including the history of liturgy, Egyptology, Assyriology, literary studies, musicology and ethnosemiotics, allows the eclectic character of litanies to be revealed, litanies which not only were a form of church prayer but also had an impact on the organization of social rituals as well as being appropriated by all the major fields of art, poetry, the fine arts and music. The musicological articles in the book address the performance of Sumerian prayers, the liturgical songs of the Middle Ages, litanies in Tudor England and polyphonic works of the great composers, such as Wolfgang Amadeus Mozart.

Litanies --- Dans l'art --- Moyen Orient. --- 264-064 --- 264-064 Smeekgebeden. Litanie van alle heiligen. Litanieën--(andere) --- Smeekgebeden. Litanie van alle heiligen. Litanieën--(andere) --- Sacred music --- Liturgics --- History. --- History and criticism. --- Christian pastoral theology

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A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier–Stokes equations, this book provides self-contained proofs of someof the most significant results in the area, many of which can only be found in researchpapers. Highlights include the existence of global-in-time Leray–Hopf weak solutionsand the local existence of strong solutions; the conditional local regularity results ofSerrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg.Appendices provide background material and proofs of some 'standard results' thatare hard to find in the literature. A substantial number of exercises are included, with fullsolutions given at the end of the book. As the only introductory text on the topic to treatall of the mainstream results in detail, this book is an ideal text for a graduate course ofone or two semesters. It is also a useful resource for anyone working in mathematicalfluid dynamics.

Navier-Stokes equations. --- Differential equations, Partial. --- Lagrange equations. --- Navier-Stokes equations.

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The rigorous mathematical theory of the Navier-Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier-Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier-Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

Differential equations, Partial. --- Navier-Stokes equations. --- Lagrange equations. --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Differential equations --- Equations of motion --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Partial differential equations