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Journal Articles Quarterly of Applied Mathematics Year : 2022

Large-time behavior of compressible polytropic fluids and nonlinear Schrödinger equation

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Abstract

In this paper we analyze the large-time behavior of weak solutions to polytropic fluid models possibly including quantum and capillary 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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Dates and versions

hal-03142668 , version 1 (16-02-2021)
hal-03142668 , version 2 (23-01-2022)

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Cite

Rémi Carles, Kleber Carrapatoso, Matthieu Hillairet. Large-time behavior of compressible polytropic fluids and nonlinear Schrödinger equation. Quarterly of Applied Mathematics, 2022, ⟨10.1090/qam/1618⟩. ⟨hal-03142668v2⟩
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