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Volume 9
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Article

A Nonhomogeneous Boundary Value Problem for Steady State Navier-Stokes Equations in a Multiply-Connected Cusp Domain

by
Kristina Kaulakytė
and
Konstantinas Pileckas
*
Institute of Applied Mathematics, Vilnius University, Naugarduko Str., 24, 03225 Vilnius, Lithuania
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(17), 2022; https://doi.org/10.3390/math9172022
Submission received: 27 July 2021 / Revised: 13 August 2021 / Accepted: 17 August 2021 / Published: 24 August 2021
(This article belongs to the Special Issue Nonlinear Boundary Value Problems and Their Applications)
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Abstract

The boundary value problem for the steady Navier–Stokes system is considered in a 2D multiply-connected bounded domain with the boundary having a power cusp singularity at the point O. The case of a boundary value with nonzero flow rates over connected components of the boundary is studied. It is also supposed that there is a source/sink in O. In this case the solution necessarily has an infinite Dirichlet integral. The existence of a solution to this problem is proved assuming that the flow rates are “sufficiently small”. This condition does not require the norm of the boundary data to be small. The solution is constructed as the sum of a function with the finite Dirichlet integral and a singular part coinciding with the asymptotic decomposition near the cusp point.
Keywords: stationary Navier–Stokes equations; multi-connected domain; power cusp; singular solutions; asymptotic expansion; regularity stationary Navier–Stokes equations; multi-connected domain; power cusp; singular solutions; asymptotic expansion; regularity

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MDPI and ACS Style

Kaulakytė, K.; Pileckas, K. A Nonhomogeneous Boundary Value Problem for Steady State Navier-Stokes Equations in a Multiply-Connected Cusp Domain. Mathematics 2021, 9, 2022. https://doi.org/10.3390/math9172022

AMA Style

Kaulakytė K, Pileckas K. A Nonhomogeneous Boundary Value Problem for Steady State Navier-Stokes Equations in a Multiply-Connected Cusp Domain. Mathematics. 2021; 9(17):2022. https://doi.org/10.3390/math9172022

Chicago/Turabian Style

Kaulakytė, Kristina, and Konstantinas Pileckas. 2021. "A Nonhomogeneous Boundary Value Problem for Steady State Navier-Stokes Equations in a Multiply-Connected Cusp Domain" Mathematics 9, no. 17: 2022. https://doi.org/10.3390/math9172022

APA Style

Kaulakytė, K., & Pileckas, K. (2021). A Nonhomogeneous Boundary Value Problem for Steady State Navier-Stokes Equations in a Multiply-Connected Cusp Domain. Mathematics, 9(17), 2022. https://doi.org/10.3390/math9172022

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