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Uniform Regularity of the Density-Dependent Incompressible MHD System in a Bounded Domain
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...
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Direction of Vorticity and a Refined Regularity Criterion for the Navier–Stokes Equations with Fractional Laplacian
We give a refined regularity criterion for solutions of the three-dimensional Navier–Stokes equations with fractional dissipative term
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Global Strong Solutions to the 3D Incompressible Heat-Conducting Magnetohydrodynamic Flows
In this article, we prove that there exists a global strong solution to the 3D inhomogeneous incompressible heat-conducting magnetohydrodynamic...
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On Wolf’s Regularity Criterion of Suitable Weak Solutions to the Navier–Stokes Equations
In this paper, we consider the local regularity of suitable weak solutions to the 3D incompressible Navier–Stokes equations. By means of the local...
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On the Existence of Classical Solution to the Steady Flows of Generalized Newtonian Fluid with Concentration Dependent Power-Law Index
Steady flows of an incompressible homogeneous chemically reacting fluid are described by a coupled system, consisting of the generalized...
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Uniqueness of Axisymmetric Viscous Flows Originating from Positive Linear Combinations of Circular Vortex Filaments
Following the recent papers by Gallay and S̆verák (Conflu Math 7:67–92,
2015 ; Uniqueness of axisymmetric viscous flows originating from circular... -
Boundary Partial \(C^{1, \alpha }\)-Regularity for Stationary Shear Thickening Flows in 3D
In this paper, we prove boundary partial regularity result for weak solutions to systems describing stationary shear thickening flows in 3D smooth...
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A Note on Prodi–Serrin Conditions for the Regularity of a Weak Solution to the Navier–Stokes Equations
The paper is concerned with the regularity of weak solutions to the Navier–Stokes equations. The aim is to show a relaxed Prodi–Serrin condition for...
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Regularity Criterion and Energy Conservation for the Supercritical Quasi-geostrophic Equation
This paper studies the regularity and energy conservation problems for the 2D supercritical quasi-geostrophic (SQG) equation. We apply an approach of...
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Asymptotics of Solutions with Vanishing at Infinity Velocity of the Steady-State Navier–Stokes Equations in the Dimension Four
The asymptotics of solutions with vanishing at infinity velocity of the steady-state Navier–Stokes equations is studied in an exterior domain
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On the Global Regularity for the 3D Magnetohydrodynamics Equations Involving Partial Components
In this paper, we study the regularity criteria of the three-dimensional magnetohydrodynamics system in terms of some components of the velocity...
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A Stationary One-Equation Turbulent Model with Applications in Porous Media
A one-equation turbulent model is studied in this work in the steady-state and with homogeneous Dirichlet boundary conditions. The considered problem...
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Pullback Asymptotic Behavior of Solutions for a 2D Non-autonomous Non-Newtonian Fluid
This paper studies the pullback asymptotic behavior of solutions for the non-autonomous incompressible non-Newtonian fluid in 2D bounded domains....