@misc{10481/81782,
year = {2023},
url = {https://hdl.handle.net/10481/81782},
abstract = {Abstract. In this paper we study the existence of finite energy traveling waves for the Gross-Pitaevskii
equation. This problem has deserved a lot of attention in the literature, but the existence of solutions
in the whole subsonic range was a standing open problem till the work of Maris¸ in 2013. However,
such result is valid only in dimension 3 and higher. In this paper we first prove the existence of finite
energy traveling waves for almost every value of the speed in the subsonic range. Our argument works
identically well in dimensions 2 and 3.
With this result in hand, a compactness argument could fill the range of admissible speeds. We
are able to do so in dimension 3, recovering the aforementioned result by Maris¸. The planar case turns
out to be more intricate and the compactness argument works only under an additional assumption on
the vortex set of the approximating solutions.},
organization = {Ministry of Education, Universities and Research (MIUR)},
organization = {Spanish Government	PGC2018-096422-B-I00},
organization = {J. Andalucia	FQM-116},
organization = {Ministry of Science and Innovation, Spain (MICINN)
Spanish Government	CEX2020-001105-M/AEI/10.13039/501100011033},
publisher = {Johns Hopkins University Press},
title = {Finite energy traveling waves for the Gross-Pitaevskii equation in the subsonic regime},
doi = {10.1353/ajm.2023.0002},
author = {Bellazzini, Jacopo and Ruiz Aguilar, David},
}