Related papers: On the Schr\"odinger flows

We establish the global well-posedness of the initial value problem for the Schrodinger map flow for maps from the real line into Kahler manifolds and for maps from the circle into Riemann surfaces. This partially resolves a conjecture of…

Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise,…

We present general results on exponential decay of finite energy solutions to stationary nonlinear Schr\"odinger equations.

We derive new results about existence and uniqueness of local and global solutions for nonlinear Schrodinger equation, including self-similar global solutions. Our analysis is performed in the framework of Marcinkiewicz spaces.

We investigate the flow of a one-dimensional nonlinear Schrodinger model with periodic boundary conditions past an obstacle, motivated by recent experiments with Bose--Einstein condensates in ring traps. Above certain rotation velocities,…

The results of this paper are twofold: In the first part, we prove that for Schr\"odinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatures, the harmonic maps which are holomorphic or…

By using the degree theory and the $\tau-$topology of Kryszewski and Szulkin, we establish a version of the Fountain Theorem for strongly indefinite functionals. The abstract result will be applied for studying the existence of infinitely…

In this note we present an algorithm to generate new Schr\" odinger type equations explicitly solvable in terms of orthogonal polynomials or associated special functions.

We prove the existence of non-trivial solutions to a system of coupled, nonlinear, Schroedinger equations with general nonlinearity.

We present basic results, known and new, on nontrivial solutions of periodic stationary nonlinear Schr\"odinger equations. We also sketch an application to nonlinear optics and discuss some open problems.

This paper studies the regularity of solutions to the Zakharov and Klein-Gordon-Schr\"{o}dinger systems at low regularity levels. The main result is that the nonlinear part of the solution flow falls in a smoother space than the initial…

We consider two types of the time-dependent Ginzburg-Landau equation in 2D bounded domains: the heat-flow equation and the Schroedinger equation. The system of ordinary differential equations is obtained that describes the evolution of the…

A significant mathematical error is identified and corrected in a recent highly-cited paper on oscillatory flows of second-grade fluids [Fetecau & Fetecau (2005). Int. J. Eng. Sci., 43, 781--789]. The corrected solutions are shown to agree…

We survey recent results on inverse boundary value problems for the magnetic Schroedinger equation.

We explain the construction of some solutions of the Stokes system with a given set of singular points, in the sense of Caffarelli, Kohn and Nirenberg. By means of a partial regularity theorem (proved elsewhere), it turns out that we are…

We consider the large time behavior in two types of equations, posed on the whole space R^d: the Schr{\"o}dinger equation with a logarithmic nonlinearity on the one hand; compressible, isothermal, Euler, Korteweg and quantum Navier-Stokes…

Strong existence and pathwise uniqueness of solutions with $L^{\infty}$-vorticity of 2D stochastic Euler equations is proved. The noise is multiplicative and involves first derivatives. A Lagrangian approach is implemented, where a…

In this note, we study an obstacle problem for the elastic flow. We prove the local-in-time existence of weak solutions and discuss their relation to classical solutions when additional regularity is obtained. Related results concerning…

We provide a natural simple argument using anistropic flows to prove the existence of weak solutions to Lutwak's $L^p$-Minkowski problem on $S^n$ which were obtained by other methods.

We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…