相关论文: Convex integration for a class of active scalar eq…

We present an algebraic model for turbulent scalar-flux vector that stems from tensor representation theory. The resulting closure contains direct dependence on mean velocity gradients and on frame rotation tensor that accounts for Coriolis…

We propose a polynomial force-motion model for planar sliding. The set of generalized friction loads is the 1-sublevel set of a polynomial whose gradient directions correspond to generalized velocities. Additionally, the polynomial is…

We develop a new boundary condition for the weak inverse mean curvature flow, which gives canonical and non-trivial solutions in bounded domains. Roughly speaking, the boundary of the domain serves as an outer obstacle, and the evolving…

The rational quantum algebraically integrable systems are non-trivial generalizations of Laplacian operators to the case of elliptic operators with variable coefficients. We study corresponding extensions of Laplacian growth connected with…

We combine classical continuum mechanics with the recently developed calculus for mixed-dimensional problems to obtain governing equations for flow in, and deformation of, fractured materials. We present models both in the context of finite…

We present a model treating the kinetics of adsorption of soluble surface-active molecules at the interface between an aqueous solution and another fluid phase. The model accounts for both the diffusive transport inside the solution and the…

We construct a model to explore the hydrodynamic interactions of active inclusions in curved biological membranes. The curved membrane is modelled as a two dimensional layer of highly viscous fluid, surrounded by external solvents of…

We consider a class of viscous fluids with a general monotone dependence of the viscous stress on the symmetric velocity gradient. We introduce the concept of dissipative solution to the associated initial boundary value problem inspired by…

We demonstrate the global existence of weak solutions to a class of semilinear strongly damped wave equations possessing nonlinear hyperbolic dynamic boundary conditions. Our work assumes $(-\Delta_W)^\theta \partial_tu$ with…

We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of…

In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on…

To our knowledge, the convex integration method has been widely applied to the study of non-uniqueness of solutions to the Naiver-Stokes equations in the periodic region, but there are few works on applying this method to the corresponding…

This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum…

We propose a new mathematical model of groundwater flow in porous medium layered over inclined impermeable bed. In its full generality, this is a free-surface problem. To obtain analytically tractable model, we use generalized…

Perturbations of fluid media can give rise to non-equilibrium dynamics, which may in turn cause motion of immersed inclusions. We consider perturbations ("activations") that are local in space and time, of a fluid density which is…

In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We study properties of these filtering flows and provide…

In this work the existence of weak solutions for a class of non-Newtonian viscous fluid problems is analyzed. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent $q$ that characterizes…

We consider strictly convex hypersurfaces which are evolving by the non-parametric logarithmic Gauss curvature flow subject to a Neumann boundary condition. Solutions are shown to converge smoothly to hypersurfaces moving by translation. In…

We are concerned with a system of partial differential equations describing internal flows of homogeneous incompressible fluids of Bingham type in which the value of activation (the so-called yield) stress depends on the internal pore…

A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid…