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Partial vanishing viscosity limit for the 2D Boussinesq system with a slip boundary condition

Liangbing Jin1, Jishan Fan2, Gen Nakamura3 and Yong Zhou1*

Author Affiliations

1 Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China

2 Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, P.R. China

3 Department of Mathematics, Hokkaido University Sapporo 060-0810, Japan

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Boundary Value Problems 2012, 2012:20  doi:10.1186/1687-2770-2012-20

Published: 15 February 2012


This article studies the partial vanishing viscosity limit of the 2D Boussinesq system in a bounded domain with a slip boundary condition. The result is proved globally in time by a logarithmic Sobolev inequality.

2010 MSC: 35Q30; 76D03; 76D05; 76D07.

Boussinesq system; inviscid limit; slip boundary condition