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The stability of Boussinesq equations with partial dissipation around the hydrostatic balance
This paper is devoted to understanding the stability of perturbations around the hydrostatic equilibrium of the Boussinesq system in order to gain insight into certain atmospheric and oceanographic phenomena. ...
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Energy conservation for the weak solutions to the 3D compressible nematic liquid crystal flow
In this paper, we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crysta...
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Normalized Solutions for Two Classes of Kirchhoff Problems with Exponential Critical Growth
In this paper, we are devoted to studying two classes of non-autonomous Kirchhoff problems with the potential term. To be precise, we assume the potential term satisfies different assumptions and the nonlinear...
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Asymptotic stability of explicit infinite energy blowup solutions of the 3D incompressible Navier-Stokes equations
In this paper, we study the dynamical stability of a family of explicit blowup solutions of the three-dimensional (3D) incompressible Navier-Stokes (NS) equations with smooth initial values, which is construct...
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Global Well-Posedness of Compressible Magneto-micropolar Fluid Equations
We are concerned with the global well-posedness of compressible magneto-micropolar fluid equations (1.1)-(1.2) in \({\mathbb {R}}^3\) ...
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Open AccessOptimal partial regularity for very weak solutions to a class of nonlinear elliptic systems
We consider optimal partial regularity for very weak solutions to a class of nonlinear elliptic systems and obtain the general criterion for a very weak solution to be regular in the neighborhood of a given po...
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Behavior of solutions to a Petrovsky equation with dam** and variable-exponent sources
This paper deals with the following Petrovsky equation with dam** and nonlinear sources: $${u_{tt}} + {\Delta ^2}u - M\left({\left\| {\nabla...
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Chapter and Conference Paper
A Correlational Strategy for the Prediction of High-Dimensional Stock Data by Neural Networks and Technical Indicators
Stock price prediction generates interesting outputs for investors. In recent years, stock technical indicators (STI) have played an important role in stock price prediction. However, the current performance o...
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Global low-energy weak solutions of the compressible magneto-micropolar fluids in the half-space
In this paper, we investigate the compressible magneto-micropolar fluids in a half-space \({\mathbb {R}}^n_+\) ...
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The MHD Equations in the Lorentz Space With Time Dependent External Forces
We are concerned with the well-posedness of the incompressible Magneto-hydrodynamical (MHD) equations in \(\mathbb {R}^n\) ...
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The Diffusive Limit of the Bipolar Vlasov–Poisson–Boltzmann Equations
In this work, we first prove the existence of the classic solutions to the dimensionless bipolar Vlasov–Poisson–Boltzmann equations by employing hypocoercive properties of the linear Boltzmann operators. Based...
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Global well-posedness for the 2D micropolar Bénard fluid system with mixed partial dissipation, angular viscosity and without thermal diffusivity
In this paper, we study the Cauchy problem of the 2D micropolar Bénard system with partial viscosity, i.e., (1) $$\mu _{12}=\mu _{21}=\gamma _...
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Optimal decay rates of the solution for generalized Poisson–Nernst–Planck–Navier–Stokes equations in \({\mathbb {R}}^3\)
The Cauchy problem of a generalized Poisson–Nernst–Planck–Navier–Stokes system in \({\mathbb {R}}^3\) ...
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Existence and Properties of Solutions for a Class of Fractional Differential Equations
In this paper, we consider the initial value problem of a class of fractional differential equations. Firstly, we obtain the existence and uniqueness of the solutions by using Picard’s method of successive app...
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The Decay Estimates for Magnetohydrodynamic Equations with Coulomb Force
In this article we consider the compressible viscous magnetohydrodynamic equations with Coulomb force. By spectral analysis and energy methods, we obtain the optimal time decay estimate of the solution. We sho...
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The Asymptotic Stability of the Solution to the Full Hall-MHD System in \(\mathbb {R}^3\)
In this paper, we consider the asymptotic stability of the solutions near a constant equilibrium state to the Cauchy problem for the compressible full Hall-MHD equations in \(\mathbb {R}^3\)R3. We employ the ener...
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Decay estimates of solutions to the bipolar compressible Euler–Poisson system in \(\pmb {\mathbb {R}^3}\)
This work is concerned with the bipolar compressible Euler–Poisson equations with dam** in three-dimensional space. We consider the optimal decay rates of the solution to the Cauchy problem, provided that th...
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A Global Existence Result for Korteweg System in the Critical LP Framework
The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin [12], which can be used as a phase transition model. Motivated...
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Retraction Note to: Global strong solution to the three-dimensional stochastic incompressible magnetohydrodynamic equations
The authors have retracted this article [1] because the article shows [2]. All authors agree to this retraction.
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A class of global large solutions to the magnetohydrodynamic equations with fractional dissipation
The global existence and regularity problem on the magnetohydrodynamic (MHD) equations with fractional dissipation is not well understood for many ranges of fractional powers. This paper examines this open pro...
