L. Chaichenets

activity

20122026

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 · 59 across the 11 of their papers we have counts for

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8 papers · 1 filter

math.AP2021

Higher order NLS with anisotropic dispersion and modulation spaces: a global existence and scattering result

Leonid Chaichenets, Nikolaos Pattakos

In this paper we transfer a small data global existence and scattering result by Wang and Hudzik to the more general case of modulation spaces $M_{p, q}^{s} (R^{d})$ where $q =…

math.AP2019★ 2 cited

On the global wellposedness of the Klein-Gordon equation for initial data in modulation spaces

Leonid Chaichenets, Nikolaos Pattakos

We prove global wellposedness of the Klein-Gordon equation with power nonlinearity $∣ u ∣^{α - 1} u$ , where $α \in [1, \frac{d}{d - 2}]$ , in dimension $d \geq 3$ with initial data i…

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.AP2019★ 2 cited

The global Cauchy problem for the NLS with higher order anisotropic dispersion

Leonid Chaichenets, Nikolaos Pattakos

We use a method developed by Strauss to obtain global wellposedness results in the mild sense for the small data Cauchy problem in modulation spaces $M_{p, q}^{s} (R^{d})$ , wher…

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

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 the modulation space $M_{p, q}^{s} (R)$ wh…

math.AP2016★ 3 cited

Local well-posedness for the nonlinear Schrödinger equation in the intersection of modulation spaces $M_{p, q}^{s} (R^{d}) \cap M_{\infty, 1} (R^{d})$

Leonid Chaichenets, Dirk Hundertmark, Peer Christian Kunstmann +1

We introduce a Littlewood-Paley characterization of modulation spaces and use it to give an alternative proof of the algebra property, somehow implicitly contained in Sugimoto (201…

math.AP2016★ 25 cited

On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space $M_{p, q} (R)$

Leonid Chaichenets, Dirk Hundertmark, Peer Kunstmann +1

We prove global existence for the one-dimensional cubic non-linear Schrödinger equation in modulation spaces $M_{p, p^{'}}$ for $p$ sufficiently close to $2$ . In contrast to known resu…

Higher order NLS with anisotropic dispersion and modulation spaces: a global existence and scattering result

On the global wellposedness of the Klein-Gordon equation for initial data in modulation spaces

On the global well-posedness of the quadratic NLS on L2(R)+H1(T)

The global Cauchy problem for the NLS with higher order anisotropic dispersion

Knocking out teeth in one-dimensional periodic NLS

Nonlinear Schrödinger equation, differentiation by parts and modulation spaces

Local well-posedness for the nonlinear Schrödinger equation in the intersection of modulation spaces Mp,qs​(Rd)∩M∞,1​(Rd)

On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space Mp,q​(R)

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

Local well-posedness for the nonlinear Schrödinger equation in the intersection of modulation spaces $M_{p, q}^{s} (R^{d}) \cap M_{\infty, 1} (R^{d})$

On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space $M_{p, q} (R)$