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In this paper, we prove some new L p L^p -estimates of the velocity by the technique of L p L^p -energy method.

First, we prove uniform-in-$ \epsilon $ regularity estimates of local strong solutions to the Chern-Simons-Schrödinger equations in $ \mathbb{R}^2 $. Here $ \epsilon $ is the dispersion coefficient. Then we prove the global well-posedness of strong solutions to the limit problem $ (\epsilon = 0) $.

In this paper, we will use the Banach fixed point theorem to prove the uniform-in-$ \epsilon $ existence of the compressible full magneto-micropolar system in a bounded smooth domain, where $ \epsilon $ is the dielectric constant. Consequently, the limit as $ \epsilon\rightarrow0 $ can be established. This approximation is usually referred to as the magnetohydrodynamics approximation and is equivalent to the neglect of the displacement current.

We prove the long time behavior of a 2D Ginzburg-Landau system in supercon-ductivity with Coulomb gauge and fixed total magnetic flux. Mathematics Subject Classifications (2020): 35A05, 35A40, 35K55, 82D55.

In this paper, we are concerned with the uniform regularity estimates of smooth solutions to the isentropic compressible magneto-micropolar system in T3. Under the assumption that , and by applying the classic bilinear commutator and product estimates, the uniform estimates of solutions to the isentropic compressible magneto-micropolar system are established in space, .

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.

In this paper we prove the local well-posedness of strong solutions to a chemotaxis-shallow water system with initial vacuum in a bounded domain Ω ų ℝ2 without the standard compatibility condition for the initial data. This improves some results obtained in [J. Differential Equations 261(2016), 6758–6789].

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).

We prove the existence of a unique solution for a time-dependent Ginzburg-Landau model in superconductivity under the Coulomb gauge. Also we prove the uniform-in-$\epsilon$ well-posedness of the solution, where $\epsilon$ is the coefficient of the double-well potential energy.

In this paper, we consider the n(n≥3)dimensional time-dependent Ginzburg–Landau model for superconductivity. First, we obtain a global existence of very weak solutions. Finally we prove a result of weak-very weak uniqueness.

In this note, we prove a new $$L^4$$ L 4 -estimate of the velocity by the technique of Hardy space $${\mathcal {H}}^1$$ H 1 and BMO.

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.

Uniform regularity estimates are proved for a compressible Gross-Pitaevskii-Navier-Stokes system in \(\mathbb {T}^n\) with \(n\ge 3\).

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.

The model system of equations which describes the self-propelled motion of point mass objects driven by camphor is a diffusion equation coupled with a system of nonlinear ordinary differential equations. If the objects have masses, then the motion of objects becomes very complicated when some of the objects hit the boundary of a water surface or collide each other. To avoid such complexity and try to get some general perspective for the motion, it is convenient to consider point mass objects, i.e., objects without areas. We give an existence of a weak solution of this model system by giving an a priori estimate for the solution. The key to this estimate is the choice of a special test function. This is a first step toward analyzing collective motion of point mass camphors. As far as we know, this result is the first result on the existence of a weak solution for this system.

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.