Related papers: Global solutions of two dimensional incompressible…
We consider the evolution of two-dimensional incompressible flows with variable density, only bounded and bounded away from zero. Assuming that the initial velocity belongs to a suitable critical subspace of L^2 , we prove a global-in-time…
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…
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…
This paper is concerned with a mathematical model which describes 2-D flows of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain. We prove the existence and uniqueness theorem for global (in time) weak solutions and…
We study the existence and uniqueness of global strong solutions to the equations of an incompressible viscoelastic fluid in a spatially periodic domain, and show that a unique strong solution exists globally in time if the initial…
We consider the Cauchy problem for incompressible viscoelastic fluids in the whole space $\mathbb{R}^d$ ($d=2,3$). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of…
This paper is dedicated to the global existence and optimal decay estimates of strong solutions to the compressible viscoelastic flows in the whole space $\mathbb{R}^n$ with any $n\geq2$. We aim at extending those works by Qian \& Zhang and…
In this paper, we are concerned with the global existence and optimal rates of strong solutions for three-dimensional compressible viscoelastic flows. We prove the global existence of the strong solutions by the standard energy method under…
The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces.…
We study the large-data Cauchy problem for two dimensional Oldroyd model of incompressible viscoelastic fluids. We prove the global-in-time existence of the Leray-Hopf type weak solutions in the physical energy space. Our method relies on a…
The global existence of solutions to incompressible viscoelastic flows has been a longstanding open problem, even for the global weak solution. Under some special structure ("div-curl" condition) the global small smooth solution was…
For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…
We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…
This paper is a continuation of our previous work (arXiv:2507.03505), where the global existence and incompressible limit of weak solutions to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density 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…
This paper establishes the global well-posedness of solutions to the Oldroyd-B model with purely horizontal viscosity and arbitrarily large initial data in two-dimensional settings, including the full space $\mathbb{R}^2$, the partially…
This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where…
The initial boundary value problem for the three-dimensional incompressible flow of liquid crystals is considered in a bounded smooth domain. The existence and uniqueness is established for both the local strong solution with large initial…
We study the initial-boundary value problem for 1D compressible MHD equations of viscous non-resistive fluids in the Lagrangian mass coordinates. Based on the estimates of upper and lower bounds of the density, weak solutions are…
We consider the initial-boundary value problem of a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities in a bounded domain $\Omega\subset\mathbb{R}^3$. Our first aim is to study…