Proving local well-posedness for quasi-linear problems in partial differential equations
presents a number of difficulties, some of which are universal and others of which are more …

We consider quasilinear, Hamiltonian perturbations of the cubic Schrödinger and of the
cubic (derivative) Klein–Gordon equations on the d-dimensional torus. If 𝜖≪ 1 is the size of …

We consider a family of Schrödinger equations with unbounded Hamiltonian quadratic
nonlinearities on a generic tori of dimension d≥ 1. We study the behavior of high Sobolev …

In this paper we provide a local well posedness result for a quasilinear beam-wave system
of equations on a one-dimensional spatial domain under periodic and Dirichlet boundary …

We provide a unified viewpoint on two illposedness mechanisms for dispersive equations in
one spatial dimension, namely degenerate dispersion and (the failure of) the Takeuchi …

The skew mean curvature flow is an evolution equation for d dimensional manifolds
embedded in R d+ 2 (or more generally, in a Riemannian manifold). It can be viewed as a …

We present a novel method for establishing large data local well-posedness in low regularity
Sobolev spaces for general quasilinear Schrödinger equations with non-degenerate and …

We prove a local in time well-posedness result for quasi-linear Hamiltonian Schrödinger
equations on T d for any d≥ 1. For any initial condition in the Sobolev space H s, with s …

We consider a completely resonant nonlinear Schrödinger equation on the d-dimensional
torus, for any d≥ 1, with polynomial nonlinearity of any degree 2 p+ 1, p≥ 1, which is gauge …

We improve the result by Feola and Iandoli (J Math Pures Appl 157: 243–281, 2022),
showing that quasilinear Hamiltonian Schrödinger type equations are well posed on H s (T …