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In this work, we prove the local well‐posedness of local strong solutions to an isentropic compressible Ginzburg–Landau–Navier–Stokes system with vacuum in a bounded domain Ω⊂R3.

In this paper, we prove global existence of strong solutions to the 2D density-dependent incompressible magnetic Benard problem in a bounded domain.

We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in ℝ3. It is proved that if the velocity field in the Besov space satisfies some integral property, then the solution keeps its smoothness.

In this paper, we prove the global well-posedness of weak and strong solutions to the nD (n≥3) phase-lock system under the Coulomb gauge.

In this paper we prove the global existence of strong solutions to a coupled chemotaxis-fluid model with subcritical sensitivity in a bounded domain $\varOmega \subset \mathbb{R}^{2} $ without small assumptions on initial data.

In this work, we consider a reduced Ginzburg–Landau model in which the magnetic field is neglected. First, we show the well-posedness of weak solutions and strong solutions in a bounded domain Ω⊂Rn. Finally, we prove the well-posedness of smooth solutions when Ω:=Rn (n≥3).

In this work, we prove some regularity criteria for a Ginzburg–Landau–Navier–Stokes system with the Coulomb gauge in a bounded domain $$\Omega \subset {\mathbb {R}}^3\,$$.

In this work, we prove the global well-posedness of strong solutions to a non-isothermal model for superconductivity in a three-dimensional domain.

This paper proves a regularity criterion for a new density-dependent incompressible Hall-MHD system with positive density.

In this paper we study the global existence of strong solutions to the 2D and 3D nonhomogeneous incompressible magnetohydrodynamic equations in a bounded domain. Our proofs are based on the combination of the regularity criterion and an abstract bootstrap argument, which provides a new way to establish the global well-posedness of strong solutions.

We prove a regularity criterion for the 3D Navier-Stokes-Allen-Cahn system in a bounded smooth domain which improves the result obtained by Y. Li, S. Ding, and M. Huang [Discrete Contin. Dyn. Syst. Ser. B, 2016, 21(5): 1507–1523]. We also present a similar result to the 3D Navier-Stokes-Cahn-Hilliard system.

In this paper, we study the low Mach number limit of a compressible non-isothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals.

In this paper, we use the bootstrap argument to prove the uniform-in- k global strong solutions of the 2D density-dependent incompressible magnetic Benard problem in a bounded domain. Here k is the heat conductivity coefficient.

In this paper, we prove some regularity criteria for the density-dependent incompressible Boussinesq and liquid crystals model. The Kato-Ponce type commutator estimates play a key role.

We prove the uniform estimates of strong solutions to a compressible full MHD- $P1$ approximate model arising in radiation magnetohydrodynamics.

In this paper, we prove the uniform regularity of the compressible full Navier–Stokes–Maxwell system in $$\mathbb {T}^3$$ .

In this paper, we prove the uniform-in-η estimates of the local strong solutions of the density-dependent incompressible MHD system in a bounded domain. Here η is the resistivity coefficient.

We prove the existence and uniqueness of global strong solutions to the Maxwell–Navier–Stokes system in a two dimensional bounded domain with Navier-type boundary condition for the velocity.

We study the initial boundary value problem for the three-dimensional modified compressible Navier–Stokes–Fourier equations proposed by Brenner. We establish a blow-up criterion for local strong solutions in terms of the density $$\rho $$ and the temperature $$\theta $$ only.

In this paper, a full incompressible magneto-micropolar system is investigated. We prove the local well-posedness of strong solutions to the full system with vacuum. Moreover, previous compatibility conditions on the initial data are also moved.

In this paper, we study the 3D compressible non-isentropic MHD equations with zero resistivity in a bounded domain. We first establish a regularity criterion for the strong solutions, and then, we combine it with an abstract bootstrap argument to prove the global well-posedness of the system under some assumptions on the viscosity coefficients and the initial data. Our results do not need the positivity of initial density, and thus, it may vanish in an open subset of the domain.

In this paper, we use the bootstrap argument to prove the uniform-in- k global strong solutions of the 2D magnetic Benard problem in a bounded domain. Here k is the heat conductivity coefficient.

In this paper we consider the 3D compressible MHD system in a bounded domain. We first prove a regularity criterion and then use it and the bootstrap argument to show the uniform-in- η global small solutions. Here η is the resistivity coefficient.

In this paper, we prove the global well‐posedness of strong solutions of the MHD system with zero resistivity in a bounded domain.

In this paper, we first prove global well-posedness of weak solutions for an epitaxial growth model with L 2 initial data in any dimension d . Then, we establish a regularity criterion of strong solutions with dimension d ≥ 3 .

In this paper, we prove the uniform-in- σ regularity for 3D time-dependent Ginzburg–Landau model in superconductivity in the case of Coulomb gauge. Here σ is the normal conductivity of the superconducting material.

This paper is contributed to the qualitative analysis of a coupled chemotaxis-fluid model on bounded domains in multiple spatial dimensions. Based on scaling-invariant argument and energy method, several optimal extensibility criteria for local classical solutions are established. As a by-product, a global well-posedness result is obtained in the two-dimensional case for general initial data.

In this paper, we prove the local well-posedness of strong solutions for a compressible Navier-Stokes-Maxwell system, provided the initial data satisfy a natural compatibility condition. We do not assume the positivity of initial density, it may vanish in an open subset (vacuum) of $Ω$.

We prove the existence and uniqueness of global strong solutions to the incompressible magneto-micropolar system in a two dimensional bounded domain with Navier type boundary condition for the velocity.

This paper proves a regularity criterion for a 3D generalized Hall-MHD system in terms of velocity gradient in negative Besov spaces.

In this paper, we consider an epitaxial growth model with slope selection and a generalized model. First, we establish some regularity criteria of strong solutions for the epitaxial growth model with slope selection. Then, we prove the global-in-time existence of smooth solutions for a generalized model.

We establish a local well-posedness and a blow-up criterion of strong solutions for the compressible Navier-Stokes-Fourier-P1 approximate model arising in radiation hydrodynamics. For the local well-posedness result, we do not need the assumption on the positivity of the initial density and it may vanish in an open subset of the domain.

This paper proves some regularity criteria for the 3D (density-dependent) incompressible MaxwellNavierStokes system, which improves a recent result of Kang and Lee (2013).

In this paper we continue our study on the establishment of uniform estimates of strong solutions with respect to the Mach number and the dielectric constant to the full compressible Navier–Stokes–Maxwell system in a bounded domain \(\Omega \subset \mathbb {R}^3\). In Fan et al. (Kinet Relat Models 9:443–453, 2016), the uniform estimates have been obtained for large initial data in a short time interval. Here we shall show that the uniform estimates exist globally if the initial data are small. Based on these uniform estimates, we obtain the convergence of the full compressible Navier–Stokes–Maxwell system to the incompressible magnetohydrodynamic equations for well-prepared initial data.

We prove a regularity criterion for the wave map in a bounded domain when the space dimension n = 2 or 3 . We also prove the global well-posedness of strong solutions for the wave map in a bounded domain when the space dimension n = 1 .

In this paper we study the low Mach number limit of the full compressible Hall-magnetohydrodynamic (Hall-MHD) system in \begin{document}$\mathbb{T}^3$\end{document} . We prove that, as the Mach number tends to zero, the strong solution of the full compressible Hall-MHD system converges to that of the incompressible Hall-MHD system.

This paper proves a new regularity criterion for a density-dependent incompressible liquid crystals model with vacuum but without any compatibility condition.

In this note, we prove a blow-up criterion for the density-dependent incompressible Euler system in a bounded domain.

In this work, we prove the local well-posedness of strong solutions to the isentropic compressible magnetohydrodynamics system with vacuum in a bounded domain Ω⊂R3.

This paper proves some regularity criteria for some simplified non-isothermal models for nematic liquid crystals.

This paper proves a regularity criterion for the 3D$3D$ full compressible Navier-Stokes-Maxwell system in a bounded domain.

We prove two new regularity criteria for the 3D incompressible Navier-Stokes equations in a bounded domain. Our results also hold for the 3D Boussinesq system with zero heat conductivity.

We first prove the uniqueness of weak solutions (ψ,A) to the 3-D Ginzburg–Landau model in superconductivity with zero magnetic diffusivity and the Coulomb gauge if (ψ,A)∈W:=(ψ,A)ψ∈L20,T;L∞∩L20,T;H1,A∈C[0,T];L3, which is a critical space for some positive constant T. We also prove the global existence of solutions when ψ0∈L∞∩W23,32 and A0∈L3. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we establish the local well-posedness and a blow-up criterion of strong solutions to the 3D compressible full Hall-MHD system with positive density.

This paper proves a new regularity criterion for a 3D density-dependent incompressible liquid crystals model with positive initial density.

In this note we prove a blow-up criterion for the full compressible Euler–Maxwell system in R 3 .

In this paper we establish some regularity criteria for the three-dimensional Boussinesq system with the temperature-dependent viscosity and thermal diffusivity in a bounded domain.