Existence of global solution to 3D density-dependent incompressible Navier-Stokes equations

Jianxia He; Ming Li; Jianxia He; Ming Li

doi:10.3934/math.2024375

AIMS Mathematics

2024, Volume 9, Issue 3: 7728-7750. doi: 10.3934/math.2024375

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Existence of global solution to 3D density-dependent incompressible Navier-Stokes equations

Jianxia He ^,,
Ming Li

Center for Nonlinear Studies, School of Mathematics, Northwest University, Xi'an 710127, China

Received: 09 November 2023 Revised: 06 January 2024 Accepted: 15 January 2024 Published: 23 February 2024
MSC : 35Q30, 76D05

In this article, we are committed to studying the three-dimensional incompressible Navier-Stokes equations, where the viscosity depends on density according to a power law. We investigate the Cauchy problem by constructing an approximation system and bootstrap argument. Finally, we establish the existence of a global strong solution under the conditions of small initial data and the compatibility condition. Meanwhile, the algebraic decay-in-time rates for the solution are also obtained. It is worth pointing out that the degradation of viscosity is allowed.
- Navier-Stokes equations,
- density-dependent viscosity,
- degenerate viscosity,
- strong solution
Citation: Jianxia He, Ming Li. Existence of global solution to 3D density-dependent incompressible Navier-Stokes equations[J]. AIMS Mathematics, 2024, 9(3): 7728-7750. doi: 10.3934/math.2024375

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Abstract

In this article, we are committed to studying the three-dimensional incompressible Navier-Stokes equations, where the viscosity depends on density according to a power law. We investigate the Cauchy problem by constructing an approximation system and bootstrap argument. Finally, we establish the existence of a global strong solution under the conditions of small initial data and the compatibility condition. Meanwhile, the algebraic decay-in-time rates for the solution are also obtained. It is worth pointing out that the degradation of viscosity is allowed.

References

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