A Weak Solution to the Navier–Stokes System with Navier’s Boundary Condition in a Time-Varying Domain

Neustupa, Jiřı́; Penel, Patrick

doi:10.1007/978-3-0348-0939-9_20

Cited by 8 publications

(6 citation statements)

References 6 publications

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“…Alternatively, the problem has been studied in [4], [5], [19], [20] by using the local transformation introduced by Inue and Wakimoto in [13], and in domains depending on time in [14]- [17].…”

Section: Mathematical Formulationmentioning

confidence: 99%

On the linear problem arising from motion of a fluid around a moving rigid body

Nečasová¹,

Wolf²

2015

Math. Bohem.

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We study a linear system of equations arising from fluid motion around a moving rigid body, where rotation is included. Originally, the coordinate system is attached to the fluid, which means that the domain is changing with respect to time. To get a problem in the fixed domain, the problem is rewritten in the coordinate system attached to the body. The aim of the present paper is the proof of the existence of a strong solution in a weighted Lebesgue space. In particular, we prove the existence of a global pressure gradient in L 2 .

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Section: Mathematical Formulationmentioning

confidence: 99%

On the linear problem arising from motion of a fluid around a moving rigid body

Nečasová¹,

Wolf²

2015

Math. Bohem.

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“…Nevertheless, the readers can find the definition of a weak solution to the problem (1.1)- (1.4) and the proof of the global in time existence of a weak solution e.g. in the papers [6] (with f = 0), [20] (in a time-varying domain Ω) and [25] (in a half-space). We repeat the definition in section 3.…”

Section: Introductionmentioning

confidence: 99%

The interior regularity of pressure associated with a weak solution to the Navier–Stokes equations with the Navier-type boundary conditions

Neustupa

Baba

2018

Journal of Mathematical Analysis and Applications

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“…The solution, provided by [3] and [20], satisfies the energy inequality. The solutions, constructed in [16] and [18], are not explicitly shown to satisfy the energy inequality, but one can observe from the proofs that they do. In this paper, we consider…”

Section: Introductionmentioning

confidence: 99%

On robustness of a strong solution to the Navier–Stokes equations with Navier’s boundary conditions in theL³-norm

Kučera

Neustupa

2017

Nonlinearity

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We recall or prove a series of results on solutions to the Navier-Stokes equation with Navier's slip boundary conditions. The main theorem says that a strong solution u on any time interval (0,T ) (where < ∞ T 0 ⩽ ) is robust in the sense that small perturbations of the initial value in the norm of Ω σ L 3 ( ) and the acting body force in the norm of Ω L T L 0, ; 2 32 ( ( )) / cause only a small perturbation of solution u in the norm of Ω L 3 ( ). This result particularly implies that the maximum length of the time interval, on which the solution starting from the initial value ∈ Ω σ u L 0 3 ( ) is regular, is a lower semi-continuous functional on Ω σ L 3 ( ).

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A Weak Solution to the Navier–Stokes System with Navier’s Boundary Condition in a Time-Varying Domain

Cited by 8 publications

References 6 publications

On the linear problem arising from motion of a fluid around a moving rigid body

On the linear problem arising from motion of a fluid around a moving rigid body

The interior regularity of pressure associated with a weak solution to the Navier–Stokes equations with the Navier-type boundary conditions

On robustness of a strong solution to the Navier–Stokes equations with Navier’s boundary conditions in theL³-norm

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A Weak Solution to the Navier–Stokes System with Navier’s Boundary Condition in a Time-Varying Domain

Cited by 8 publications

References 6 publications

On the linear problem arising from motion of a fluid around a moving rigid body

On the linear problem arising from motion of a fluid around a moving rigid body

The interior regularity of pressure associated with a weak solution to the Navier–Stokes equations with the Navier-type boundary conditions

On robustness of a strong solution to the Navier–Stokes equations with Navier’s boundary conditions in theL3-norm

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On robustness of a strong solution to the Navier–Stokes equations with Navier’s boundary conditions in theL³-norm