Global existence of strong solutions to compressible Navier-Stokes-Korteweg equations with external potential force

Kaile Chen; Yunyun Liang; Nengqiu Zhang; Kaile Chen; Yunyun Liang; Nengqiu Zhang

doi:10.3934/math.20231418

AIMS Mathematics

2023, Volume 8, Issue 11: 27712-27724. doi: 10.3934/math.20231418

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Research article

Global existence of strong solutions to compressible Navier-Stokes-Korteweg equations with external potential force

1.
School of information and mathematics, Yangtze University, Jingzhou 434023, China
2.
School of Science, East China University of Science and Technology, Shanghai 200237, China
Correction on: AIMS Mathematics 9: 5480–5481.

Received: 03 August 2023 Revised: 18 September 2023 Accepted: 24 September 2023 Published: 08 October 2023
MSC : 34B40, 35Q35, 93D20

In this article, we consider a three dimensional compressible Navier-Stokes-Korteweg equations with the effect of external potential force. Under the smallness assumptions on both the external potential force and the initial perturbation of the stationary solution in $ H^2(\mathbb{R}^3)\times H^1(\mathbb{R}^3) $, we prove the global existence and regularity of strong solutions for the Navier-Stokes-Korteweg equations.
- Navier-Stokes-Korteweg equations,
- stationary solution,
- global existence
Citation: Kaile Chen, Yunyun Liang, Nengqiu Zhang. Global existence of strong solutions to compressible Navier-Stokes-Korteweg equations with external potential force[J]. AIMS Mathematics, 2023, 8(11): 27712-27724. doi: 10.3934/math.20231418

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Abstract

In this article, we consider a three dimensional compressible Navier-Stokes-Korteweg equations with the effect of external potential force. Under the smallness assumptions on both the external potential force and the initial perturbation of the stationary solution in $ H^2(\mathbb{R}^3)\times H^1(\mathbb{R}^3) $, we prove the global existence and regularity of strong solutions for the Navier-Stokes-Korteweg equations.

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