Advances in Differential Equations

Analysis of the existence for the steady Navier-Stokes equations with anisotropic diffusion

S.N. Antontsev and H.B. de Oliveira

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Abstract

The boundary-value problem for the generalized Navier-Stokes equations with anisotropic diffusion is considered in this work. For this problem, we prove the existence of weak solutions in the sense that solutions and test functions are considered in the same admissible function space. We also prove the existence of very weak solutions, i.e., solutions for which the test functions have more regularity. By exploiting several examples we show, in the case of dimension $3$, that these existence results improve its isotropic versions in almost all directions or for particular choices of all the diffusion coefficients.

Article information

Source
Adv. Differential Equations Volume 19, Number 5/6 (2014), 441-472.

Dates
First available in Project Euclid: 3 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.ade/1396558058

Mathematical Reviews number (MathSciNet)
MR3189091

Zentralblatt MATH identifier
1291.82119

Subjects
Primary: 35J60: Nonlinear elliptic equations 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]

Citation

Antontsev, S.N.; de Oliveira, H.B. Analysis of the existence for the steady Navier-Stokes equations with anisotropic diffusion. Adv. Differential Equations 19 (2014), no. 5/6, 441--472. https://projecteuclid.org/euclid.ade/1396558058.


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