Related papers: Note on Global Regularity for 2D Oldroyd-B Fluids …
We prove global existence of strong solutions to the drift-diffusion-Maxwell system in two space dimension. We also provide an exponential growth estimate for the $H^1$ norm of the solution.
This paper is devoted to the uniform vanishing damping limit of the 2D inviscid Oldroyd-B model with fractional stress tensor diffusion. Firstly, we find that fractional stress tensor diffusion helps to reduce the global regularity of the…
We give a small data global well-posedness result for an incompressible Oldroyd-B model with wave number dissipation in the equation of stress tensor. The result is uniform in solvent Reynolds numbers, and requires only fractional…
We report evidence of irregular unsteady flow of two-dimensional polymer solutions in the absence of inertia in cross-slot geometry using numerical simulations of Oldroyd-B model. By exploring the transition to time-dependent flow versus…
In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…
We consider the initial-boundary value problem for an incompressible Oldroyd-B model with stress diffusion in two-dimensional upper half plane which describes the motion of viscoelastic polymeric fluids. From the physical point of view, the…
This paper establishes the global existence and regularity for a system of the two-dimensional (2D) magnetohydrodynamic (MHD) equations with only directional hyperresistivity. More precisely, the equation of $b_1$ (the horizontal component…
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…
The system under study is a solute-solvent-structure (SSS) interaction problem for the interaction of a dilute three-dimensional Oldroyd-B polymeric fluid with a two-dimensional viscoelastic shell. We show that a unique global strong…
This article represents the second installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on global solutions for small and localized data. Such…
We show a global existence result of weak solutions for a class of generalized Surface Quasi-Geostrophic equation in the inviscid case. We also prove the global regularity of such solutions for the equation with slightly supercritical…
In this paper we study the global regularity of the following 2D (two-dimensional) generalized magnetohydrodynamic equations \begin{eqnarray*} \left\{\begin{array}{llll} u_t + u \cdot \nabla u & = & - \nabla p + b \cdot \nabla b - \nu…
In this paper, we consider the finite difference method for the generalized two-dimensional (2D) multi-term time-fractional Oldroyd-B fluid model, which is a subclass of non-Newtonian fluids. Different from the general multi-term time…
This paper is devoted to the study of the regularity of solutions to some systems of reaction--diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without…
The global existence of classical solutions to reaction-diffusion systems in dimensions one and two is proved. The considered systems are assumed to satisfy an {\it entropy inequality} and have nonlinearities with at most cubic growth in 1D…
In this paper we are concerned with the global existence of smooth solutions to the turbulent flow equations for compressible flows in $\mathbb{R}^3$. The global well-posedness is proved under the condition that the initial data are close…
We consider the problem of a 3D-3D-2D mutually coupled solute-solvent-structure three-states system. This describes the interaction of a flexible structure with a polymeric fluid of classical Oldroyd-B type without centre-of-mass diffusion.…
Exact and approximate expressions are established for dissipation, the power of the shear stress at the wall and the boundary layer thickness corresponding to the motion of an Oldroyd-B fluid induced by a constantly accelerating plate. The…
As a continuation of the previous work [40], in this paper we focus on the Cauchy problem of the two-dimensional (2D) incompressible Boussinesq equations with fractional Laplacian dissipation. We give an elementary proof of the global…
In this paper, we prove the global $C^\infty$ regularity of the Oleinik's solution for the steady Prandtl equation with favorable pressure.