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Large time behavior of strong solutions to the 1D non-resistive full compressible MHD system with large initial data
The Cauchy and initial-boundary value problems for one-dimensional compressible magnetohydrodynamics (MHD) system with non-resistive are studied in...
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Global well-posedness for the incompressible MHD equations with density-dependent viscosity and resistivity coefficients
This paper concerns an initial–boundary value problem of the inhomogeneous incompressible MHD equations in a smooth bounded domain. The viscosity and...
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Local well-posedness to inhomogeneous Ericksen–Leslie system with general Leslie stress tensor
In this paper, we establish the local well-posedness of strong solutions to the Cauchy problem of the density-dependent liquid crystal system, with...
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Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel–Navier–Stokes system
This paper deals with an initial-boundary value problem in a two-dimensional smoothly bounded domain for the Keller–Segel–Navier–Stokes system with...
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Global existence for a degenerate haptotaxis model of cancer invasion
We propose and study a strongly coupled PDE–ODE system with tissue-dependent degenerate diffusion and haptotaxis that can serve as a model prototype...
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Global classical solutions of 3D isentropic compressible MHD with general initial data
In this paper, we consider the Cauchy problem of three-dimensional isentropic compressible magnetohydrodynamic equations with general initial data...
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Life span of solutions of a weakly coupled parabolic system
We consider the Cauchy problem for the weakly coupled parabolic system ∂ t w λ −Δ w λ = F( w λ ) in R N , where λ > 0, w λ = ( u ...
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On a regularity criterion in terms of the gradient of pressure for the Navier-Stokes equations in \(\mathbb{R}^{N}\)
In this paper we establish a Serrin’s type regularity criterion on the gradient of pressure for weak solutions to the Navier–Stokes equations in
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Asymptotic behaviour of large solutions of quasilinear elliptic problems
The paper deals with the large solutions of the problems $\triangle u=u^p$ and $\triangle u= e^u.$ They blow up at the boundary. It is well-known...
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Existence and continuous dependence of large solutions for the magnetohydrodynamic equations
Global solutions of the nonlinear magnetohydrodynamic (MHD) equations with general large initial data are investigated. First the existence and...
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Energy estimates and uniqueness of the weak solutions of initial-boundary value problems for semilinear hyperbolic systems
Bounds in energy for the smooth solutions of initial and boundary value problems for semilinear hyperbolic systems are given. We prove that the...
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About a one-dimensional stationary Schrödinger-Poisson system with Kohn-Sham potential
The stationary Schrödinger-Poisson system with a self-consistent effective Kohn-Sham potential is a system of PDEs for the electrostatic potential...
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Phragmen-Lindelöf type results for second order quasilinear parabolic equations in ℝ2
In this paper Phragmen-Lindelöf type growth-decay estimates are derived for solutions of initial-boundary value problems associated with a class of...