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Article
Editorial introduction to the special issue “Plasma physics in the 20th century as told by players”
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Article
A contemporary look at Hermann Hankel’s 1861 pioneering work on Lagrangian fluid dynamics
The present paper is a companion to the paper by Villone and Rampf (2017), titled “Hermann Hankel’s On the general theory of motion of fluids, an essay including an English translation of the complete Preisschri...
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Article
A Constructive Approach to Regularity of Lagrangian Trajectories for Incompressible Euler Flow in a Bounded Domain
The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may...
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Article
Cauchy’s almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to Göttingen University, contain major discoveries on vorticity dynamics w...
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Article
A Very Smooth Ride in a Rough Sea
It has been known for some time that a 3D incompressible Euler flow that has initially a barely smooth velocity field nonetheless has Lagrangian fluid particle trajectories that are analytic in time for at lea...
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Book
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Chapter
The Equations of Fluid Dynamics and Some of Their Consequences
It is well known that the overwhelming majority of both natural and man-made flows of fluids do not vary smoothly in space and time but fluctuate in a quite disordered manner, exhibiting sudden and irregular (...
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Chapter
More About Linear Stability Theory: Studies of The Initial-Value Problem
The normal-mode method of the linear stability theory, which was considered in Chap. 2, deals only with special “wave-like” infinitesimal disturbances of a given laminar...
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Chapter
Further Weakly-Nonlinear Approaches to Laminar-Flow Stability: Blasius Boundary-Layer Flow as a Paradigm
Landau’s equation and its generalizations considered in Sect. 4.2 represent a particular weakly-nonlinear approach to the study of flow stability, based on the assumptio...
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Chapter
Basic Experimental Facts and Introduction to Linear Stability Theory
Equations describing fluid motion, and some of their simpler solutions, can be found in particular in Sect. 1 of the book by Monin and Yaglom (1971) (later referred as MYl). It is also pointed out there that thes...
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Chapter
Stability to Finite Disturbances: Energy Method and Landau’s Equation
The main part of Chap. 2 and the whole of Chap. 3 were devoted to topics of linear stability theory dealing with the evolution of very small flow disturbances satisfying the linearized fluid dynamics equations...
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Article
Open AccessEntire Solutions of Hydrodynamical Equations with Exponential Dissipation
We consider a modification of the three-dimensional Navier–Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation o...
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Book
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Book
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Article
A reconstruction of the initial conditions of the Universe by optimal mass transportation
Reconstructing the density fluctuations in the early Universe that evolved into the distribution of galaxies we see today is a challenge to modern cosmology1. An accurate reconstruction would allow us to test cos...
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Book and Conference Proceedings
Advances in Turbulence VII
Proceedings of the Seventh European Turbulence Conference, held in Saint-Jean Cap Ferrat, France, 30 June – 3 July 1998 / Actes de la Septième Conférence Européenne de Turbulence, tenue à Saint-Jean Cap Ferrat, France, 30 Juin – 3 Juillet 1998
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Book and Conference Proceedings
Lévy Flights and Related Topics in Physics
Proceedings of the International Workshop Held at Nice, France, 27–30 June 1994
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Chapter and Conference Paper
Universality of escape from a half-space for symmetrical random walks
A new proof is given that a one-dimensional random walk starting from the origin, with independent steps having an even p.d.f. K(x), has a probability p n , of never visiting the ne...
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Chapter and Conference Paper
Summary of the Symposium
I would like to share with you some things that I heard at this meeting, and I heard a great deal. Maybe you can correct me if you did not hear them, that might be useful. We started off talking about intuitio...
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Article
The inviscid Burgers equation with initial data of Brownian type
The solutions to Burgers equation, in the limit of vanishing viscosity, are investigated when the initial velocity is a Brownian motion (or fractional Brownian motion) function, i.e. a Gaussian process with sc...
