Work

On Properties of Statistically Stationary Solutions to the One-Dimensional Schrödinger Map Equation.

Year: 2026

Type: article

Abstract: We investigate further qualitative properties of statistically stationary solutions to the Schrödinger map equation (SME) and the Binormal Curvature Flow (BCF) on a bounded interval, continuing the work initiated by E. G., M. Hofmanová [25]. Concerning the statistically stationary solutions to the SME, we show that the laws of some relevant observables (such as the space average and the energy) are absolutely continuous with respect to the Lebesgue measure, with a Gaussian decay property for the energy. We further prove that the law $$\mu $$ μ of the statistically stationary solution has dimension of at least two: this means that any compact set of Hausdorff dimension smaller than two has $$\mu $$ μ -measure zero. These properties, with appropriate modifications of the norms, pass directly to the statistically stationary solutions to the BCF.

Source: Journal of Dynamics and Differential Equations

DOI: 10.1007/s10884-026-10526-x

Authors: Emanuela Gussetti, Mouhamadou Sy

Institutions: Bielefeld University, African Institute for Mathematical Sciences

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Alexander von Humboldt-Stiftung, Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung