Volume 35, Issue 1
Blow-up of Classical Solutions to the Isentropic Compressible Barotropic Navier-Stokes-Langevin-Korteweg Equations

J. Part. Diff. Eq., 35 (2022), pp. 78-86.

Published online: 2021-10

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• Abstract

In this paper, we study the barotropic Navier-Stokes-Langevin-Korteweg system in $\mathbb{R}^{3}$. Assuming  the derivatives of the square root of the density and the velocity field decay to zero at infinity, we can prove the classical solutions blow up in finite time when the initial energy has a certain upper bound. We obtain this blow up result by a contradiction argument based on the conservation of the total mass and the total quasi momentum.

• Keywords

Navier-Stokes-Langevin-Korteweg system classical solutions blow up.

35Q35, 35B44

17110180002@fudan.edu.cn (Ke Hu)

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@Article{JPDE-35-78, author = {Hu , Ke}, title = {Blow-up of Classical Solutions to the Isentropic Compressible Barotropic Navier-Stokes-Langevin-Korteweg Equations}, journal = {Journal of Partial Differential Equations}, year = {2021}, volume = {35}, number = {1}, pages = {78--86}, abstract = {

In this paper, we study the barotropic Navier-Stokes-Langevin-Korteweg system in $\mathbb{R}^{3}$. Assuming  the derivatives of the square root of the density and the velocity field decay to zero at infinity, we can prove the classical solutions blow up in finite time when the initial energy has a certain upper bound. We obtain this blow up result by a contradiction argument based on the conservation of the total mass and the total quasi momentum.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v35.n1.5}, url = {http://global-sci.org/intro/article_detail/jpde/19910.html} }
TY - JOUR T1 - Blow-up of Classical Solutions to the Isentropic Compressible Barotropic Navier-Stokes-Langevin-Korteweg Equations AU - Hu , Ke JO - Journal of Partial Differential Equations VL - 1 SP - 78 EP - 86 PY - 2021 DA - 2021/10 SN - 35 DO - http://doi.org/10.4208/jpde.v35.n1.5 UR - https://global-sci.org/intro/article_detail/jpde/19910.html KW - Navier-Stokes-Langevin-Korteweg system KW - classical solutions KW - blow up. AB -

In this paper, we study the barotropic Navier-Stokes-Langevin-Korteweg system in $\mathbb{R}^{3}$. Assuming  the derivatives of the square root of the density and the velocity field decay to zero at infinity, we can prove the classical solutions blow up in finite time when the initial energy has a certain upper bound. We obtain this blow up result by a contradiction argument based on the conservation of the total mass and the total quasi momentum.

Ke Hu. (2021). Blow-up of Classical Solutions to the Isentropic Compressible Barotropic Navier-Stokes-Langevin-Korteweg Equations. Journal of Partial Differential Equations. 35 (1). 78-86. doi:10.4208/jpde.v35.n1.5
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