Vanishing viscosity limit of incompressible flow around a small obstacle: A special case

Xiaoguang You; Xiaoguang You

doi:10.3934/math.2023135

AIMS Mathematics

2023, Volume 8, Issue 2: 2611-2621. doi: 10.3934/math.2023135

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Vanishing viscosity limit of incompressible flow around a small obstacle: A special case

Xiaoguang You ^,

School of Mathematics, Northwest University, Xi'an 710069, China

Received: 13 September 2022 Revised: 27 October 2022 Accepted: 01 November 2022 Published: 08 November 2022
MSC : 35Q30, 76D05, 76D10

In this paper, we consider two dimensional viscous flow around a small obstacle. In ^[4], the authors proved that the solutions of the Navier-Stokes system around a small obstacle of size $ \varepsilon $ converge to solutions of the Euler system in the whole space under the condition that the size of the obstacle $ \varepsilon $ is smaller than a suitable constant $ K $ times the kinematic viscosity $ \nu $. We show that, if the Euler flow is antisymmetric, then this smallness condition can be removed.
- Navier-Stokes equations,
- Euler equations,
- vanishing viscosity limit,
- exterior domain,
- boundary layer
Citation: Xiaoguang You. Vanishing viscosity limit of incompressible flow around a small obstacle: A special case[J]. AIMS Mathematics, 2023, 8(2): 2611-2621. doi: 10.3934/math.2023135

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Abstract

In this paper, we consider two dimensional viscous flow around a small obstacle. In ^[4], the authors proved that the solutions of the Navier-Stokes system around a small obstacle of size $ \varepsilon $ converge to solutions of the Euler system in the whole space under the condition that the size of the obstacle $ \varepsilon $ is smaller than a suitable constant $ K $ times the kinematic viscosity $ \nu $. We show that, if the Euler flow is antisymmetric, then this smallness condition can be removed.

References

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