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Online ISSN 1552-4485; Print ISSN 0033-569X
Large-time behavior of compressible polytropic fluids and nonlinear Schrödinger equation
Authors:
Rémi Carles, Kleber Carrapatoso and Matthieu Hillairet
Journal:
Quart. Appl. Math. 80 (2022), 549-574
MSC (2020):
Primary 35B40, 35D30, 35Q30, 35Q31, 35Q55
DOI:
https://doi.org/10.1090/qam/1618
Published electronically:
March 15, 2022
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we analyze the large-time behavior of weak solutions to polytropic fluid models possibly including quantum and viscous effects. Formal a priori estimates show that the density of solutions to these systems should disperse with time. Scaling appropriately the system, we prove that, under a reasonable assumption on the decay of energy, the density of weak solutions converges in large times to an unknown profile. In contrast with the isothermal case, we also show that there exists a large variety of asymptotic profiles. We complement the study by providing existence of global-in-time weak solutions satisfying the required decay of energy. As a byproduct of our method, we also obtain results concerning the large-time behavior of solutions to nonlinear Schrödinger equation, allowing the presence of a semi-classical parameter as well as long range nonlinearities.
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Additional Information
Rémi Carles
Affiliation:
Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
ORCID:
0000-0002-8866-587X
Email:
Remi.Carles@math.cnrs.fr
Kleber Carrapatoso
Affiliation:
CMLS,École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau cedex, France
MR Author ID:
1043725
Email:
kleber.carrapatoso@polytechnique.edu
Matthieu Hillairet
Affiliation:
Institut Montpelliérain Alexander Grothendieck, Univ Montpellier, CNRS, Montpellier, France
MR Author ID:
718943
Email:
matthieu.hillairet@umontpellier.fr
Received by editor(s):
October 7, 2021
Received by editor(s) in revised form:
January 13, 2022
Published electronically:
March 15, 2022
Additional Notes:
The first author was supported by Rennes Métropole, through its AIS program. The second author was supported by the Project EFI (ANR-17-CE40-0030) of the French National Research Agency (ANR). The third author was supported by Institut Universitaire de France and SingFlows project (ANR-18- CE40-0027) of the French National Research Agency (ANR)
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