This textbook introduces the well-posedness theory for initial-value problems of nonlinear,
dispersive partial differential equations, with special focus on two key models, the Korteweg …

In this article we study the pointwise decay properties of solutions to the wave equation on a
class of stationary asymptotically flat backgrounds in three space dimensions. Under the …

In this article, we study the pointwise decay properties of solutions to the wave equation on a
class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the …

This paper is devoted to the well-posedness of stochastic nonlinear Schrödinger equations
in the energy space H 1 (R d), and is a continuation of our recent work (Barbu et al., 2014) …

We prove well-posedness results for stochastic nonlinear Schrödinger equations with linear
multiplicative Wiener noise, including the nonconservative case. Our approach is different …

The limiting absorption principle asserts that if H is a suitable Schrödinger operator, and f
lives in a suitable weighted L 2 space (namely H^ 0, 1/2+ σ H 0, 1/2+ σ for some σ> 0 σ> 0) …

We prove Strichartz estimates for the Schrödinger equation with an electromagnetic
potential, in dimension n⩾ 3. The decay and regularity assumptions on the potentials are …

We consider abstract non-negative self-adjoint operators on L 2 (X) which satisfy the finite-
speed propagation property for the corresponding wave equation. For such operators, we …

We obtain a representation formula for solutions to Schrödinger equations with a class of
homogeneous, scaling-critical electromagnetic potentials. As a consequence, we prove the …

In this article we consider variable coefficient time dependent wave equations in R * R^ n.
Using phase space methods we construct outgoing parametrices and prove Strichartz type …