On global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum

On global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum

Abstract In this paper, by using the energy estimates, the structure of the equations, and the properties of one dimension, we establish the global existence and uniqueness of strong and classical solutions to the initial boundary value problem of compressible Navier–Stokes/Allen–Cahn system in one-...

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Main Author: Menglong Su
Format: article
Language:EN
Published: SpringerOpen 2021
Subjects:
Analysis
QA299.6-433
Online Access:https://doaj.org/article/86b4053775a64f3e9f852018bcee2218
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spelling oai:doaj.org-article:86b4053775a64f3e9f852018bcee22182021-11-21T12:07:12ZOn global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum10.1186/s13661-021-01570-11687-2770https://doaj.org/article/86b4053775a64f3e9f852018bcee22182021-11-01T00:00:00Zhttps://doi.org/10.1186/s13661-021-01570-1https://doaj.org/toc/1687-2770Abstract In this paper, by using the energy estimates, the structure of the equations, and the properties of one dimension, we establish the global existence and uniqueness of strong and classical solutions to the initial boundary value problem of compressible Navier–Stokes/Allen–Cahn system in one-dimensional bounded domain with the viscosity depending on density. Here, we emphasize that the time does not need to be bounded and the initial vacuum is still permitted. Furthermore, we also show the large time behavior of the velocity.Menglong SuSpringerOpenarticleAnalysisQA299.6-433ENBoundary Value Problems, Vol 2021, Iss 1, Pp 1-21 (2021)
institution DOAJ
collection DOAJ
language EN
topic Analysis
QA299.6-433
spellingShingle Analysis
QA299.6-433
Menglong Su
On global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum
description Abstract In this paper, by using the energy estimates, the structure of the equations, and the properties of one dimension, we establish the global existence and uniqueness of strong and classical solutions to the initial boundary value problem of compressible Navier–Stokes/Allen–Cahn system in one-dimensional bounded domain with the viscosity depending on density. Here, we emphasize that the time does not need to be bounded and the initial vacuum is still permitted. Furthermore, we also show the large time behavior of the velocity.
format article
author Menglong Su
author_facet Menglong Su
author_sort Menglong Su
title On global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum
title_short On global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum
title_full On global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum
title_fullStr On global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum
title_full_unstemmed On global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum
title_sort on global classical solutions to one-dimensional compressible navier–stokes/allen–cahn system with density-dependent viscosity and vacuum
publisher SpringerOpen
publishDate 2021
url https://doaj.org/article/86b4053775a64f3e9f852018bcee2218
work_keys_str_mv AT menglongsu onglobalclassicalsolutionstoonedimensionalcompressiblenavierstokesallencahnsystemwithdensitydependentviscosityandvacuum
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