Part I. Foundations: 1. Random variables 2. Probability measures 3. Stochastic processes 4. The stochastic integral Part II. Existence and Uniqueness: 5. Linear equations with additive noise 6. Linear equations with multiplicative noise 7. Existence and uniqueness for nonlinear equations 8. Martingale solutions Part III. Properties of Solutions: 9. Markov properties and Kolmogorov equations 10. Absolute continuity and Girsanov's theorem 11. Large time behaviour of solutions 12. Small noise asymptotic.

Stochastic Equations in Infinite Dimensions

We present a general method which enables us to prove the orbital stability of some standing waves in nonlinear Schrodinger equations. For example, we treat the cases of nonlinear Schrodinger equations arising in laser beams, of time-dependent Hartree equations ....

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Orbital stability of standing waves for some nonlinear Schrödinger equations

The Cauchy problem for the critical nonlinear Schro¨dinger equation in H s

Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system

This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering

Weak and Measure-Valued Solutions to Evolutionary PDEs

The equations of Navier-Stokes and abstract parabolic equations

Estimating ∇u by div u and curl u

On the regularity of the pressure of weak solutions of Navier-Stokes equations

is a formally selfadjoint positive elliptic operator and f is a real C2-function with non-negative primitive function. We treat both the homogeneous initialboundary value problem over IR+ x f2 for a smooth open set ~2clR" and the Cauchy problem over IR+ x 1R ~ For the initial-boundary value problem we show that any strong solution of (0.1), known to exist according to Heinz and yon Wahl [4] if 2rn f (J) (u2)=O(lul~-2J) , j = 0 , 1 , [u[~oo,

Wolf von Wahl

Papers

The equations of Navier-Stokes and abstract parabolic equations

Estimating ∇u by div u and curl u

On the regularity of the pressure of weak solutions of Navier-Stokes equations

Global Classical Solutions of Nonlinear Wave Equations.

L p-Decay rates for homogeneous wave-equations