相关论文: Weak solutions to the time-fractional g-B\'enard e…

We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three spatial dimensions, we first prove the existence of…

We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$…

This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier-Stokes…

We investigate the heat equation with a time-dependent, anisotropic, and potentially singular diffusivity tensor. Since weak (in the Sobolev sense) or distributional solutions may not exist in this setting, we employ the framework of very…

We investigate the heat equation with a time-dependent, anisotropic, and potentially singular diffusivity tensor. Since weak (in the Sobolev sense) or distributional solutions may not exist in this setting, we employ the framework of very…

In this paper, we intend to reveal how the fractional dissipation $(-\Delta)^{\alpha}$ affects the regularity of weak solutions to the 3d generalized Navier-Stokes equations. Precisely, it will be shown that the $(5-4\alpha)/2\alpha$…

We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally speaking, the proof is based on the new weighted…

In this paper, we derive the time-fractional Cahn-Hilliard equation from continuum mixture theory with a modification of Fick's law of diffusion. This model describes the process of phase separation with nonlocal memory effects. We analyze…

We study the non-uniqueness of weak solutions for the two-dimensional hyper-dissipative Navier-Stokes equations in the super-critical spaces $L_{t}^{\gamma}L_{x}^{p}$ when $\alpha\in[1,\frac{3}{2})$, and obtain the conclusion that the…

We prove existence of weak solutions of a fractional thin film type equation in any space dimension and for any order of the equation. The proof is based on a gradient flow technique in the space of Borel probability measures endowed with…

We present and analyze a space-time Petrov-Galerkin finite element method for a time-fractional diffusion equation involving a Riemann-Liouville fractional derivative of order $\alpha\in(0,1)$ in time and zero initial data. We derive a…

In this paper, the initial-boundary value problem to the three-dimensional inhomogeneous, incompressible and heat-conducting Navier-Stokes equations with temperature-depending viscosity coefficient is considered in a bounded domain. The…

This paper concerns the existence of global weak solutions \`a la Leray for compressible Navier-Stokes equations with a pressure law that depends on the density and on time and space variables $t$ and $x$. The assumptions on the pressure…

We study a diffuse-interface model that describes the dynamics of two-phase incompressible flows driven by the thermo-induced Marangoni effect. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity, the…

We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method…

We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. The underlying relative energy inequality holds as an equality for classical solutions and if the additional variable vanishes, these…

We consider the flow of a generalized non-Newtonian incompressible heat-conducting fluid in a~bounded two-dimensional domain, subject to Dirichlet boundary conditions for velocity and temperature. The fluid obeys a power-law constitutive…

This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet…

In this paper, we study the initial value problem of the Navier-Stokes equations in the half-space. Let a solenoidal initial velocity be given in the function space $ \dot{B}_{pq,0}^{\alpha-\frac{2}{2}}({\mathbb R}^n_+)$ for $\alpha +1 =…

We study a time--space nonlocal diffusion equation driven by additive time--space white noise, where the time derivative is the Caputo derivative of order $\alpha\in(0,2)$. The model couples local diffusion with a nonlocal convolution…