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In this paper, we investigate the global existence and uniqueness of strong solutions to the two‐dimensional Boussinesq‐MHD equations without the temperature diffusion for general initial data in Hm$$ {H}^m $$ with m>2$$ m>2 $$. As an application, we shall prove the propagation of the Hm+1$$ {H}^{m+1} $$ regularity of the interface between fluids with different temperatures. [ABSTRACT FROM AUTHOR]

In this article, we study the global well‐posedness and large‐time behaviors of solutions to the two‐dimensional tropical climate system with zero thermal diffusion for small initial data in the whole space. The main approaches include high‐ and low‐frequency decomposition method and exploiting the structure of system (1) to obtain the estimates of thermal dissipation. We utilize the time decay properties of the kernels to a linear differential equation to obtain the decay rates of solutions of the low‐frequency part and the decay property of exponential operator for the high‐frequency part. The key ingredient here is the explicit large‐time decay rate of solutions. [ABSTRACT FROM AUTHOR]

This paper examines the initial-value problem for the nonhomogeneous incompressible nematic liquid crystals system with vacuum. This paper establishes two main results. The first result is involved with the global strong solutions to the 2D liquid crystals system in a bounded smooth domain. Our second result is concerned with the small data global existence result about the 3D system in the whole space. In addition, the local existence and a blow-up criterion of strong solutions are also mentioned. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]