On the asymptotic behavior of<i>D</i>-solutions of the plane steady-state Navier–Stokes equations

Russo, Antonio

doi:10.2140/pjm.2010.246.253

Cited by 15 publications

(15 citation statements)

References 2 publications

(3 reference statements)

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“…This result is improved by Russo [27]. Then Galdi and Simader [12] considered the problem for external force f (x) with little regularity, and Galdi and Sohr [13], Sazonov [31] and Russo [26] obtained precise asymptotic behavior of w(x) and π(x). (For more complete references, see Galdi [11].)…”

Section: Introductionmentioning

confidence: 94%

Existence and Uniqueness of Weak Solutions to the Two-Dimensional Stationary Navier–Stokes Exterior Problem

Yamazaki

2018

J. Math. Fluid Mech.

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This paper is concerned with the stationary Navier-Stokes equation in two-dimensional exterior domains with external forces and inhomogeneous boundary conditions, and shows the existence of weak solutions. This solution enjoys a new energy inequality, provided the total flux is bounded by an absolute constant. It is also shown that, under the symmetry condition, the weak solutions tend to 0 at infinity. This paper also provides two criteria for the uniqueness of weak solutions under the assumption on the existence of one small solution which vanishes at infinity. In these criteria the aforementioned energy inequality plays a crucial role.

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Section: Introductionmentioning

confidence: 94%

Existence and Uniqueness of Weak Solutions to the Two-Dimensional Stationary Navier–Stokes Exterior Problem

Yamazaki

2018

J. Math. Fluid Mech.

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“…Then Gilbarg and Weinberger and Amick considered this problem. In particular, considered the case

Ω is invariant under the mapping π_{1} : (x_{1}, x_{2}) \mapsto (- x_{1}, x_{2})

and

w_{1} (- x_{1}, x_{2}) = - w_{1} (x_{1}, x_{2}), w_{2} (- x_{1}, x_{2}) = w_{2} (x_{1}, x_{2}) .

Next, Galdi and Simader considered the problem for external force

f (x)

with little regularity, and Galdi and Sohr , Sazonov and A. Russo obtained precise asymptotic behavior of

u (x)

and

p (x)

. (For more complete references, see Galdi .…”

Section: Introductionmentioning

confidence: 99%

Two‐dimensional stationary Navier–Stokes equations with 4‐cyclic symmetry

Yamazaki

2016

Mathematische Nachrichten

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This paper is concerned with the stationary Navier–Stokes equation in the whole plane and in the two–dimensional exterior domain invariant under the action of the cyclic group of order 4, and gives a condition on the potentials yielding the external force, and on the boundary value, sufficient for the unique existence of a small solution equivariant with respect to the aforementioned cyclic group.

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“…As we already pointed out, the problem is that the solution to the Stokes equation with boundary data u * = 0 diverges at infinity, unless one makes additional assumptions on the domain B and the data u * . Partial results for the Navier Stokes system with symmetric data can be found in [8,18,19,17] .…”

Section: Introductionmentioning

confidence: 99%