Jean Van Schaftingen

activity

20072023

most citedGroundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics

890 citations · 3.5k across the 69 of their papers we have counts for

collaborators

Showing 2015 · math.APShow all

4 papers · 2 filters

math.AP2015★ 57 cited

Least action nodal solutions for the quadratic Choquard equation

Marco Ghimenti, Vitaly Moroz, Jean Van Schaftingen

We prove the existence of a minimal action nodal solution for the quadratic Choquard equation $- Δ u + u = (I_{α} * ∣ u ∣^{2}) u in R^{N},$ where $I_{α}$ is…

math.AP2015★ 3 cited

Applications of Bourgain-Brezis inequalities to Fluid Mechanics and Magnetism

Sagun Chanillo, Jean Van Schaftingen, Po-lam Yung

We apply the borderline Sobolev inequalities of Bourgain-Brezis to the vorticity equation and Navier-Stokes equation in 2D. We take the initial vorticity to be in the space of func…

math.AP2015★ 216 cited

Nodal solutions for the Choquard equation

Marco Ghimenti, Jean Van Schaftingen

We consider the general Choquard equations $- Δ u + u = (I_{α} * ∣ u ∣^{p}) ∣ u ∣^{p - 2} u$ where $I_{α}$ is a Riesz potential. We construct minimal action odd solutions for $p \in (\fr…

math.AP2015★ 3 cited

Geometric partial differentiability on manifolds: the tangential derivative and the chain rule

Alexandra Convent, Jean Van Schaftingen

We define the tangential derivative, a notion of directional derivative which is invariant under diffeomorphisms. In particular this derivative is invariant under changes of chart…