Related papers: Convex integration for a class of active scalar eq…
In most fluid dynamics problems, the governing equations are nonlinear because of the presence of convective terms. Nevertheless, existence of solutions can be shown by direct sum provided one identifies, in the relevant Banach space of…
For any $0\leq \gamma < 1/5$, we construct weak solutions $(v, B, p )$ of the Ideal MHD Equations which do not conserve the total kinetic energy, the cross-helicity and lie in $C^\gamma(\mathbb{T}^3\times\mathbb{R})$. In the spirit of…
One proves existence and uniqueness of strong solutions to stochastic porous media equations under minimal monotonicity conditions on the nonlinearity. In particular, we do not assume continuity of the drift or any growth condition at…
We consider the mixed formulation of the equations governing Darcy-Forchheimer flow in porous media. We prove existence and uniqueness of a solution for the stationary problem and the existence of a solution for the transient problem.
We survey recent results in the mathematical literature on the equations of incompressible fluid dynamics, highlighting common themes and how they might contribute to the understanding of some phenomena in the theory of fully developed…
We study a nonlinear fluid-structure interaction problem in which the fluid is described by the three-dimensional incompressible Navier-Stokes equations, and the elastic structure is modeled by the nonlinear plate equation which includes a…
Microfluidics involves the manipulation of flows at the microscale, typically requiring external power sources to generate pressure gradients. Alternatively, harnessing flows from active fluids, which are usually chaotic, has been proposed…
We consider the dynamics of particle systems where the particles are confined by impenetrable barriers to a bounded, possibly non-convex domain $\Omega$. When particles hit the boundary, we consider an instant change in velocity, which…
We show that weak convergence of point measures and $(2+\epsilon)$-moment conditions imply hydrodynamic equations at the limit of infinitely many interacting molecules. The conditions are satisfied whenever the solutions of the classical…
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like…
Non-unique weak solutions in Leray-Hopf class are constructed for the three dimensional magneto-hydrodynamics with Hall effect. We adapt the widely appreciated convex integration framework developed in a recent work of Buckmaster and Vicol…
In this paper, new classes of functions are defined. These spaces generalize Morrey spaces and give a refinement of Lebesgue spaces. Some embeddings between these new classes are also proved. Finally, the authors apply these classes of…
A numerical solution is presented for the natural convection from inclined wall plumes which arise from a line thermal source imbedded at the leading edge of an adiabatic plate with arbitrary tilt angle and embedded in a fluid-saturated…
In this paper we analyze the interaction of an incompressible Newtonian fluid with a linearly elastic Koiter shell whose motion is restricted to transverse displacements. The middle surface of the shell constitutes the mathematical boundary…
The approach allowing is considered to represent the solutions such as stationary lonely waves of various nonlinear wave the equations as system of the ordinary differential equations in variable action - angle.
In this study, we develop computational models and methodology for accurate multi-component-flow simulation in under-resolved multi-scale porous structures. It is generally impractical to fully resolve the flow in porous structures with…
The stochastic dynamics of a rigid inclusion constrained to move on a curved surface has many applications in biological and soft matter physics, ranging from the diffusion of passive or active membrane proteins to the motion of phoretic…
We prove the existence and uniqueness of entropy solutions for nonlinear diffusion equations with nonlinear conservative gradient noise. As particular applications our results include stochastic porous media equations, as well as the…
Compaction in reactive porous media is modelled as a reaction-diffusion process with a moving boundary. Asymptotic analysis is used to find solutions for the coupled nonlinear compaction equations, and a traveling wave solution is obtained…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…