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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Perfect Incompressible Fluids (Hardcover)
Loot Price: R6,178
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Perfect Incompressible Fluids (Hardcover)
Series: Oxford Lecture Series in Mathematics and Its Applications, 14
Expected to ship within 12 - 17 working days
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The aim of this book is to offer a direct and self-contained access
to some of the new or recent results in fluid mechanics. It gives
an authoritative account on the theory of the Euler equations
describing a perfect incompressible fluid. First of all, the text
derives the Euler equations from a variational principle, and
recalls the relations on vorticity and pressure. Various weak
formulations are proposed. The book then presents the tools of
analysis necessary for their study: Littlewood-Paley theory, action
of Fourier multipliers on L spaces, and partial differential
calculus. These techniques are then used to prove various recent
results concerning vortext patches or sheets, essentially the
persistence of the smoothness of the boundary of a vortex patch,
even if that smoothness allows singular points, as well as the
existence of weak solutions of the vorticity sheet type. The text
also presents properties of microlocal (analytic or Gevrey)
regularity of the solutions of Euler equations, and provides links
of such properties to the smoothness in time of the flow of the
solution vector field.
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