Global well-posedness of the 1d compressible Navier–Stokes system with rough data

Ke Chen; Ly Kim Ha; Ruilin Hu; Quoc Hung Nguyen

doi:10.1016/j.matpur.2023.09.012

Global well-posedness of the 1d compressible Navier–Stokes system with rough data

Ke Chen
, Ly Kim Ha
, Ruilin Hu
, Quoc Hung Nguyen

Department of Mathematical Sciences

Fudan University
University of Science VNU-HCMC
Vietnam National University
Chinese Academy of Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the global well-posedness problem for the 1d compressible Navier–Stokes systems (cNSE) in gas dynamics with rough initial data. First, Liu and Yu (2022) [30] established the global well-posedness theory for the 1d isentropic cNSE with initial velocity data in BV space. Then, it was extended to the 1d full cNSE with initial velocity and temperature data in BV space by Wang et al. (2022) [31]. We improve the global well-posedness result of Liu and Yu with initial velocity data in W^2γ,1 space; and of Wang–Yu–Zhang with initial velocity data in L²∩W^2γ,1 space and initial data of temperature in [Formula presented] for any γ>0 arbitrarily small. Our essential ideas are based on establishing various “end-point” smoothing estimates for the 1d parabolic equation.

Original language	English
Pages (from-to)	425-453
Number of pages	29
Journal	Journal de Mathématiques Pures et Appliquées
Volume	179
Early online date	21 Sept 2023
DOIs	https://doi.org/10.1016/j.matpur.2023.09.012
Publication status	Published - 30 Nov 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Masson SAS

Keywords

Compressible Navier- Stokes
Weak solution
Well-posedness

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1016/j.matpur.2023.09.012

Cite this

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title = "Global well-posedness of the 1d compressible Navier–Stokes system with rough data",

abstract = "In this paper, we study the global well-posedness problem for the 1d compressible Navier–Stokes systems (cNSE) in gas dynamics with rough initial data. First, Liu and Yu (2022) [30] established the global well-posedness theory for the 1d isentropic cNSE with initial velocity data in BV space. Then, it was extended to the 1d full cNSE with initial velocity and temperature data in BV space by Wang et al. (2022) [31]. We improve the global well-posedness result of Liu and Yu with initial velocity data in W2γ,1 space; and of Wang–Yu–Zhang with initial velocity data in L2∩W2γ,1 space and initial data of temperature in [Formula presented] for any γ>0 arbitrarily small. Our essential ideas are based on establishing various “end-point” smoothing estimates for the 1d parabolic equation.",

keywords = "Compressible Navier- Stokes, Weak solution, Well-posedness",

author = "Ke Chen and Ha, \{Ly Kim\} and Ruilin Hu and Nguyen, \{Quoc Hung\}",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Masson SAS",

year = "2023",

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doi = "10.1016/j.matpur.2023.09.012",

language = "English",

volume = "179",

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TY - JOUR

T1 - Global well-posedness of the 1d compressible Navier–Stokes system with rough data

AU - Chen, Ke

AU - Ha, Ly Kim

AU - Hu, Ruilin

AU - Nguyen, Quoc Hung

PY - 2023/11/30

Y1 - 2023/11/30

N2 - In this paper, we study the global well-posedness problem for the 1d compressible Navier–Stokes systems (cNSE) in gas dynamics with rough initial data. First, Liu and Yu (2022) [30] established the global well-posedness theory for the 1d isentropic cNSE with initial velocity data in BV space. Then, it was extended to the 1d full cNSE with initial velocity and temperature data in BV space by Wang et al. (2022) [31]. We improve the global well-posedness result of Liu and Yu with initial velocity data in W2γ,1 space; and of Wang–Yu–Zhang with initial velocity data in L2∩W2γ,1 space and initial data of temperature in [Formula presented] for any γ>0 arbitrarily small. Our essential ideas are based on establishing various “end-point” smoothing estimates for the 1d parabolic equation.

AB - In this paper, we study the global well-posedness problem for the 1d compressible Navier–Stokes systems (cNSE) in gas dynamics with rough initial data. First, Liu and Yu (2022) [30] established the global well-posedness theory for the 1d isentropic cNSE with initial velocity data in BV space. Then, it was extended to the 1d full cNSE with initial velocity and temperature data in BV space by Wang et al. (2022) [31]. We improve the global well-posedness result of Liu and Yu with initial velocity data in W2γ,1 space; and of Wang–Yu–Zhang with initial velocity data in L2∩W2γ,1 space and initial data of temperature in [Formula presented] for any γ>0 arbitrarily small. Our essential ideas are based on establishing various “end-point” smoothing estimates for the 1d parabolic equation.

KW - Compressible Navier- Stokes

KW - Weak solution

KW - Well-posedness

UR - https://www.scopus.com/pages/publications/85173152226

U2 - 10.1016/j.matpur.2023.09.012

DO - 10.1016/j.matpur.2023.09.012

M3 - Article

AN - SCOPUS:85173152226

SN - 0021-7824

VL - 179

SP - 425

EP - 453

JO - Journal de Mathématiques Pures et Appliquées

JF - Journal de Mathématiques Pures et Appliquées

ER -

Global well-posedness of the 1d compressible Navier–Stokes system with rough data

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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