P. Kunstmann

activity

20102021

most citedOn existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space

M_{p, q} (R)

25 citations · 70 across the 13 of their papers we have counts for

collaborators

13 papers

math.AP2021

Global wellposedness of NLS in $H^{1} (R) + H^{s} (T)$

Friedrich Klaus, Peer Kunstmann

We show global wellposedness for the defocusing cubic nonlinear Schrödinger equation (NLS) in $H^{1} (R) + H^{3/2 +} (T)$ , and for the defocusing NLS with polynomial n…

math.AP2019★ 1 cited

Unconditional uniqueness of higher order nonlinear Schrödinger equations

Friedrich Klaus, Peer Kunstmann, Nikolaos Pattakos

We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic fourth order nonlinear Schrödinger equation with initial data $u_{0} \in X$ , where…

math.AP2019★ 2 cited

On the global well-posedness of the quadratic NLS on $L^{2} (R) + H^{1} (T)$

Leonid Chaichenets, Dirk Hundertmark, Peer Christian Kunstmann +1

We study the one dimensional nonlinear Schrödinger equation with power nonlinearity $∣ u ∣^{α - 1} u$ for $α \in [1, 5]$ and initial data $u_{0} \in L^{2} (R) + H^{1} (T)$ . We…

math-ph2018★ 6 cited

Cwikel's bound reloaded

Dirk Hundertmark, Peer Kunstmann, Tobias Ried +1

There are a couple of proofs by now for the famous Cwikel--Lieb--Rozenblum (CLR) bound, which is a semiclassical bound on the number of bound states for a Schrödinger operator, pro…

math.AP2018★ 4 cited

Knocking out teeth in one-dimensional periodic NLS

Leonid Chaichenets, Dirk Hundertmark, Peer Kunstmann +1

We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schrödinger equation in one dimension with initial data $u_{0}$ in $H^{s…

math.AP2018★ 12 cited

Nonlinear Schrödinger equation, differentiation by parts and modulation spaces