Non-existence of classical solutions with finite energy to the Cauchy problem of the Navier–Stokes–Korteweg equations-Reference-Cited by-同舟云学术

Non-existence of classical solutions with finite energy to the Cauchy problem of the Navier–Stokes–Korteweg equations

Published:2022-04-01 Issue:4 Volume:63 Page:041511
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:J. Math. Phys.

Author:

Tang Tong¹^ORCID

Affiliation:

1. School of Mathematical Science, Yangzhou University, Yangzhou 225002, People’s Republic of China

Abstract

This paper concerns the compressible Navier–Stokes–Korteweg equations. Based on previous work [Li et al., Arch. Ration. Mech. Anal. 232, 557–590 (2019)], we prove that the classical solution with finite energy does not exist in the inhomogeneous Sobolev space for any short time under some natural assumptions on initial data near the vacuum.

Funder

NSFC

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://aip.scitation.org/doi/pdf/10.1063/5.0083048

Reference33 articles.

1. The Quantum Hydrodynamics System in Two Space Dimensions

2. Global Existence of Finite Energy Weak Solutions of Quantum Navier–Stokes Equations

3. Relaxation Limit from the Quantum Navier–Stokes Equations to the Quantum Drift–Diffusion Equation

4. On Some Compressible Fluid Models: Korteweg, Lubrication, and Shallow Water Systems

5. On the existence of global weak solutions to the Navier–Stokes equations for viscous compressible and heat conducting fluids

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On Well-Posedness of Quantum Fluid Systems in the Class of Dissipative Solutions;SIAM Journal on Mathematical Analysis;2023-06-21

2. On the blow‐up phenomena of the compressible Navier‐Stokes‐Korteweg system with degenerate viscosity;Mathematical Methods in the Applied Sciences;2022-11-28