Global weak solutions to the three-dimensional inviscid Boussinesq system in the presence of magnetic field



In this paper, we consider the inviscid Boussinesq system in the presence of magnetic field in three space dimensions. We prove that the system admits infinitely many global weak solutions with large initial data. Our main tool is based on the convex integration method developed by De Lellis and Székelyhidi in the context of incompressible Euler system.


Boussinesq system Weak solutions Convex integration 

Mathematics Subject Classification

35M11 35D30 



The research of Y. Li is supported by China Scholarship Council under Grant Number 201806190103; he is also indebted to the Institute of Mathematics of the Czech Academy of Sciences for the invitation and hospitality. The author thanks Professor Eduard Feireisl for guidance and fruitful discussions, together with the anonymous referees for carefully reading of the manuscript and helpful comments.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesAnhui UniversityHefeiPeople’s Republic of China

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