相关论文: Struwe-like solutions for an evolutionary model of…

This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as…

In this paper, we consider a two-dimensional non-resistive magnetohydrodynamic model, taking the fluctuation of absolute temperature into account. Combining the method of weak convergence developed by Lions [20], Feireisl et al. [7, 8] from…

We prove the global existence of weak solutions to the Navier-Stokes equations of compressible heat-conducting fluids in two spatial dimensions with initial data and external forces which are large and spherically symmetric. The solutions…

We prove the existence of strong time-periodic solutions and their asymptotic stability with the total energy of the perturbations decaying to zero at an exponential decay rate as $t \rightarrow \infty$ for a semilinear (nonlinearly…

The continuity of the kinetic energy is an important property of incompressible viscous fluid flows. We show that for any prescribed finite energy divergence-free initial data there exist infinitely many global in time weak solutions with…

This paper investigates the long-time dynamics of solutions for an abstract nonlinear stochastic hydrodynamic-type equation driven by multiplicative L\'{e}vy noise. The framework encompasses several key hydrodynamical models, including the…

We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…

The evolution of two partially miscible, nonhomogeneous, incompressible viscous fluids of non-Newtonian type, can be governed by the Navier-Stokes-Cahn-Hilliard system. In the present work, we prove the global existence of weak solutions…

We study the incompressible stationary Navier-Stokes equations in the upper-half plane with homogeneous Dirichlet boundary condition and non-zero external forcing terms. Existence of weak solutions is proved under a suitable condition on…

We consider a system of nonlinear partial differential equations modeling the unsteady motion of an incompressible generalized Newtonian fluid with chemical reactions. The system consists of the generalized Navier-Stokes equations with…

In a previous paper [Jayanti, P.C., Trivisa, K. Local Existence of Solutions to a Navier-Stokes-Nonlinear-Schr\"odinger Model of Superfluidity. J. Math. Fluid Mech. 24, 46 (2022)], the authors proved the existence of local-in-time weak…

We consider here an elliptic coupled system describing the dynamics of liquid crystals flows. This system is posed on the whole n-dimensional space. We introduce first the notion of very weak solutions for this system. Then, within the…

This paper concerns the existence of global weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients. We construct suitable approximate system which has smooth solutions satisfying the…

This paper establishes a regularity theory for the magnetohydrodynamics (MHD) equations with external forces through scaling analysis. Inspired by the existing methodology, we utilize linearized approximations and the monotonicity property…

We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…

So far existence of dissipative weak solutions for the compressible Navier-Stokes equations (i.e. weak solutions satisfying the relative energy inequality) is known only in the case of boundary conditions with non zero inflow/outflow (i.e.,…

In this paper, the system of particles coupled with fluid is considered. The particles are described by a Vlasov equation, and the fluid is governed by a forced Navier-Stokes equations. The interaction with fluid phase governed by…

Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…

The paper considers a system of equations that models a lateral flow of a Boussinesq--Scriven fluid on a passively evolving surface embedded in $\mathbb{R}^3$. For the resulting Navier-Stokes type system, posed on a smooth closed…

We are concerned with compressible magneto-micropolar fluid equations (1.1)-(1.2). The global existence and large time behaviour of solutions near a constant state to the magneto-micropolar-Navier-Stokes-Poisson (MMNSP) system is…