Journal of Nonlinear Mathematical Physics

Volume 10, Issue Supplement 1, August 2003

The Öresund Symposium on Partial Differential Equations

Lund, May 23-25, 2002

Foreword and list of participants

1. Navier­Stokes Equations with Nonhomogeneous Dirichlet Data

Herbert AMANN
Pages: 1 - 11
We discuss the solvability of the time-dependent incompressible Navier­Stokes equtions with nonhomogeneous Dirichlet data in spaces of low regularity.

2. The Cauchy Problem for the Nonlinear Schrödinger Equation on a Compact Manifold

Nicolas BURQ, Patrick GÉRARD, Nikolay TZVETKOV
Pages: 12 - 27
We discuss the wellposedness theory of the Cauchy problem for the nonlinear Schrödinger equation on compact Riemannian manifolds. New dispersive estimates on the linear Schrödinger group are used to get global existence in the energy space on arbirary surfaces and three-dimensional manifolds, generalizing...

3. The Intermediate Surface Diffusion Flow on Spheres

Joachim ESCHER
Pages: 28 - 46
It is shown that solutions to the intermediate surface diffusion flow are real analytic in space and time, provided the initial surface is real diffeomorphic to a Euclidean sphere.

4. Ehrenpreis Type Representations and Their Riemann­Hilbert Nonlinearisation

Athanassios S FOKAS
Pages: 47 - 61
We review a new method for studying boundary value problems for evolution PDEs. This method yields explicit results for a large class of evolution equations which iclude: (a) Linear equations with constant coefficients, (b) certain classes of linear equations with variable coefficients, and (c) integrable...

5. The Derivative Nonlinear Schrödinger Equation in Analytic Classes

Pages: 62 - 71
The derivative nonlinear Schrödinger equation is shown to be locally well-posed in a class of functions analytic on a strip around the real axis. The main feature of the result is that the width of the strip does not shrink in time. To overcome the derivative loss, Kato-type smoothing results and...

6. The Classical Problem of Water Waves: a Reservoir of Integrable and Nearly-Integrable Equations

Pages: 72 - 92
In this contribution, we describe the simplest, classical problem in water waves, and use this as a vehicle to outline the techniques that we adopt to analyse this particular approach to the derivation of soliton-type equations. The surprise, perhaps, is that such an apparently transparent set of...

7. Essential Spectrum Due to Singularity

Pages: 93 - 106
It is proven that the essential spectrum of any self-adjoint operator associated with the matrix differential expression

8. On a Two-Parameter Extension of the Lattice KdV System Associated with an Elliptic Curve

Pages: 107 - 123
A general structure is developed from which a system of integrable partial difference equations is derived generalising the lattice KdV equation. The construction is based on an infinite matrix scheme with as key ingredient a (formal) elliptic Cauchy kernel. The consistency and integrability of the...