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Scattering for 1D cubic NLS and singular vortex dynamics

Valeria Banica, Luis Vega (2012)

Journal of the European Mathematical Society

We study the stability of self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These particular solutions χ a ( t , x ) form a family of evolving regular curves in ℝ 3 that develop a singularity in finite time, indexed by a parameter a > 0 . We consider curves that are small regular perturbations of χ a ( t 0 , x ) for a fixed time t 0 . In particular, their curvature is not vanishing at infinity, so we are not in the context of known results of local existence...

Scattering of small solutions of a symmetric regularized-long-wave equation

Sevdzhan Hakkaev (2004)

Applicationes Mathematicae

We study the decay in time of solutions of a symmetric regularized-long-wave equation and we show that under some restriction on the form of nonlinearity, the solutions of the nonlinear equation have the same long time behavior as those of the linear equation. This behavior allows us to establish a nonlinear scattering result for small perturbations.

Smoothness of the motion of a rigid body immersed in an incompressible perfect fluid

Olivier Glass, Franck Sueur, Takéo Takahashi (2012)

Annales scientifiques de l'École Normale Supérieure

We consider the motion of a rigid body immersed in an incompressible perfect fluid which occupies a three-dimensional bounded domain. For such a system the Cauchy problem is well-posed locally in time if the initial velocity of the fluid is in the Hölder space C 1 , r . In this paper we prove that the smoothness of the motion of the rigid body may be only limited by the smoothness of the boundaries (of the body and of the domain). In particular for analytic boundaries the motion of the rigid body is analytic...

Some inverse and control problems for fluids

Enrique Fernández-Cara, Thierry Horsin, Henry Kasumba (2013)

Annales mathématiques Blaise Pascal

This paper deals with some inverse and control problems for the Navier-Stokes and related systems. We will focus on some particular aspects that have recently led to interesting (theoretical and numerical) results: geometric inverse problems, Eulerian and Lagrangian controllability and vortex reduction oriented to shape optimization.

Some methodical remarks concerning the flow around arbitrary profiles

Ilja Černý (1982)

Aplikace matematiky

Two well known definitions of the flow of a plane vector field around the boundary of a region Ω are compared. The definition (appropriately arranged) based on the constantness of the stream function on every profile is not only invariant under conformal mappings but more general than the definition based on the vanishing of the normal component of the field on ∂ Ω .

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