Harmonic Maps and Ideal Fluid Flows

Aleman, A.; Constantin, A.
May 2012
Archive for Rational Mechanics & Analysis;May2012, Vol. 204 Issue 2, p479
Academic Journal
Using harmonic maps we provide an approach towards obtaining explicit solutions to the incompressible two-dimensional Euler equations. More precisely, the problem of finding all solutions which in Lagrangian variables (describing the particle paths of the flow) present a labelling by harmonic functions is reduced to solving an explicit nonlinear differential system in $${\mathbb {C^n}}$$ with n = 3 or n = 4. While the general solution is not available in explicit form, structural properties of the system permit us to identify several families of explicit solutions.


Related Articles

  • Classifications of some special infinity-harmonic maps. Ze-Ping Wang; Ye-Lin Ou // Balkan Journal of Geometry & Its Applications;2009, Vol. 14 Issue 1, p120 

    ∞-Harmonic maps are a generalization of ∞-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic ∞-harmonic maps from and into a sphere, quadratic...

  • Uniformly distributed ridge approximation of some classes of harmonic functions. Babenko, V.; Levchenko, D. // Ukrainian Mathematical Journal;Mar2013, Vol. 64 Issue 10, p1621 

    We determine the exact values of the uniformly distributed ridge approximation of some classes of harmonic functions of two variables.

  • EXTENSION DES FONCTIONS PLURISOUSHARMONIQUES A TRAVERS DE "PETITS" SOUS-ENSEMBLES. Jamel, Abidi // Publications de l'Institut Mathematique;2010, Vol. 88 Issue 102, p123 

    No abstract available.

  • An entremum problem. SIMONS, STUART // Mathematical Gazette;Jul2013, Vol. 97 Issue 539, p306 

    The article discusses an entremum problem in the field of mathematics. It focuses on how to find the quadrilaterals with the maximum area. It employs the Lagrange method of undetermined multipliers to solve for the stationary values of a function of two variables that are connected by a single...

  • Multibubble analysis on N-Laplace equation in $${\mathbb{R}^N}$$. Adimurthi; Yang, Yunyan // Calculus of Variations & Partial Differential Equations;Jan2011, Vol. 40 Issue 1/2, p1 

    In this note, we describe the asymptotic behavior of sequences of solutions to N-Laplace equations with critical exponential growth in smooth bounded domain in $${\mathbb{R}^N}$$. Precisely we prove multibubble phenomena and obtain an energy inequality for those concentrating solutions. In fact...

  • New Classes of Salagean type Meromorphic Harmonic Functions. Bostanci, Hakan; �zt�rk, Metin // International Journal of Mathematics Sciences;Winter2008, Vol. 2 Issue 1, p52 

    In this paper, a necessary and sufficient coefficient are given for functions in a class of complex valued meromorphic harmonic univalent functions of the form f = h + ? using Salagean operator. Furthermore, distortion theorems, extreme points, convolution condition and convex combinations for...

  • $$\varepsilon $$ -regularity for systems involving non-local, antisymmetric operators. Schikorra, Armin // Calculus of Variations & Partial Differential Equations;Dec2015, Vol. 54 Issue 4, p3531 

    We prove an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side. These systems contain as special cases, both, Euler-Lagrange equations of conformally invariant variational functionals as Rivière treated them, and...

  • Minimal dimension families of complex lines sufficient for holomorphic extension of functions. Kytmanov, A.; Myslivets, S.; Kuzovatov, V. // Siberian Mathematical Journal;Mar2011, Vol. 52 Issue 2, p256 

    We consider continuous functions given on the boundary of a bounded domain D in â„‚, n > 1, with the one-dimensional holomorphic extension property along families of complex lines. We study the existence of holomorphic extensions of these functions to D depending on the dimension and...

  • Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field. J. Palacián // Celestial Mechanics & Dynamical Astronomy;Aug2007, Vol. 98 Issue 4, p219 

    Abstract  We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is caused by its...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics