Mathematical Topics in Fluid Mechanics: Incompressible Models, Vol. 1
One of the most challenging topics in applied mathematics is the development of the theory of nonlinear partial different equations. Many problems in mechanics, geometry, and probability lead to such equations when formulated in mathematical terms. Yet despite a long history of contributions, no core theory has been formulated. Written by the winner of the 1994 Fields Medal, this outstanding two-volume work helps shed new light on this important topic. Volume 1 emphasizes the mathematical...
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One of the most challenging topics in applied mathematics is the development of the theory of nonlinear partial different equations. Many problems in mechanics, geometry, and probability lead to such equations when formulated in mathematical terms. Yet despite a long history of contributions, no core theory has been formulated. Written by the winner of the 1994 Fields Medal, this outstanding two-volume work helps shed new light on this important topic. Volume 1 emphasizes the mathematical analysis of incompressible models. After recalling the fundamental description of Newtonian fluids, a profound and self-contained study of both the classical Navier-Stokes equations (including the inhomogeneous case) and the Euler equations is given. Results about the existence and regularity of solutions are presented with complete proofs. The text highlights in particular the use of modern analytical tools and methods, and it indicates many open problems. Mathematical Topics in Fluid Mechanics will be an indispensable reference for every researcher in the field. Its topicality and the clear, concise presentations by the author make it an outstanding contribution to the great theoretical problems concerning mathematical modelling of physical phenomena. Booknews Not a comprehensive treatment but a selection of the most significant mathematical results on fluid mechanics models. Limited to newtonian liquids. Describes density-dependent and other Navier-Stokes equations, Euler equations, and other incompressible models. Assumes only training in nonlinear partial differential equations. The second of the two volumes considers compressible models and asymptotic problems. Annotation c. by Book News, Inc., Portland, Or.
Preface Table of contents1. Presentation of the models Part 1: Incompressible Models2. Density-dependent Navier-Stokes equations3. Navier-Stokes equations4. Euler equations and other incompressible models Appendix A Truncation of divergence-free vectorfields Appendix B Two facts on D1,2(R2)Appendix C Compactness in time with values in weak topologies Appendix D Weak L1 estimates for solutions of the heat equationAppendix E A short proof of the existence of renormalized solutions for parabolic equations Intended Table of Contents of Volume 2Part 2: Compressible Models5. Compactness results for compressible isentropic Navier-Stokes6. Stationary problems7. Existence results8. Related questions Part 3: Asymptotic limites9. Asymptotic limits
\ BooknewsNot a comprehensive treatment but a selection of the most significant mathematical results on fluid mechanics models. Limited to newtonian liquids. Describes density-dependent and other Navier-Stokes equations, Euler equations, and other incompressible models. Assumes only training in nonlinear partial differential equations. The second of the two volumes considers compressible models and asymptotic problems. Annotation c. by Book News, Inc., Portland, Or.\ \
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