相关论文: Well-posedness for 2D non-homogeneous incompressib…
The present paper is concerned with the well-posedness theory for non-homogeneous incompressible fluids exhibiting odd (non-dissipative) viscosity effects. Differently from previous works, we consider here the full odd viscosity tensor.…
In this paper, we study a system of PDEs describing the motion of two compressible viscous fluids occupying the whole space $\mathbb R^d\;(d\in \{2,3\}$). The two phases of the mixture are separated by a $\mathscr{C}^{1+\alpha}$-regular…
Several fluid systems are characterised by time reversal and parity breaking. Examples of such phenomena arise both in quantum and classical hydrodynamics. In these situations, the viscosity tensor, often dubbed ``odd viscosity'', becomes…
In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…
This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in $\R^{N}$ with $N\geq2$. We address the question of well-posedness for {\it large} data having critical Besov regularity…
This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields. We consider an initial-boundary value problem for both compressible and…
We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the…
We investigate global strong solutions for the incompressible viscoelastic system of Oldroyd--B type with the initial data close to a stable equilibrium. We obtain the existence and uniqueness of the global solution in a functional setting…
In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing…
We investigate local and global strong solutions for the incompressible viscoelastic system of Oldroyd--B type. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated…
Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a…
We discuss the linear hydrodynamic response of a two-dimensional active chiral compressible fluid with odd viscosity. The viscosity coefficient represents broken time-reversal and parity symmetries in the 2D fluid and characterizes the…
In this paper, the authors first establish the global well-posedness of strong solutions of the simplified Ericksen-Leslie model for nonhomogeneous incompressible nematic liquid crystal flows in two dimensions if the initial data satisfies…
We are concerned with the well-posedness of the density-dependent incompressible viscoelastic fluid system. By Schauder-Tychonoff fixed point argument, when $\|{1}/{\rho_0}-1\|_{\dot{B}_{p,1}^{{N}/{p}}}$ is small, local well-posedness is…
The nonhomogeneous incompressible Magnetohydrodynamic Equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with slip boundary conditions. The key is the constraint of an additional initial value…
In this paper, we are concerned with the global well-posedness of 3D inhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity when the initial velocity is sufficiently small in the critical Besov space…
We establish global well-posedness of strong solutions for the nonhomogeneous magnetohydrodynamic equations with density-dependent viscosity and initial density allowing vanish in two-dimensional (2D) bounded domains. Applying delicate…
In this paper, we are concerned with the three-dimensional nonhomogeneous B\'enard system with density-dependent viscosity in bounded domain. The global well-posedness of strong solution is established, provided that the initial total mass…
In this paper, we consider the three-dimensional full compressible viscous non-resistive MHD system. Global well-posedness is proved for an initial-boundary value problem around a strong background magnetic field. It is also shown that the…
We consider the two-dimensional incompressible inhomogeneous Navier-Stokes equations with odd viscosity, where the shear and the odd viscosity coefficients depend continuously on the unknown density function. We establish the existence of…