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We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We…
The dynamics and stability of a thin gas layer moving between two fluid layers moving in the same or opposite direction is studied. The linear evolutionary equations describing the spatial-temporal dynamics of the interface perturbations…
In a first order theory of dissipative hydrodynamics, we have simulated hydrodynamic evolution of QGP fluid with dissipation due to shear viscosity only. Simulation confirms that compared to an ideal fluid, energy density or temperature of…
Let $X_0, \widetilde{X}$ be two smooth, closed and locally convex curves in the plane with same winding number. A curvature flow with a nonlocal term is constructed to evolve $X_0$ into $\widetilde{X}$. It is proved that this flow exits…
Elasto-inertial turbulence is a new state of turbulence found in flows with polymer additives . The dynamics of turbulence generated and controlled by such additives is investigated from the perspective of the coupling between polymer…
We investigate the motion of a family of closed curves evolving according to the geometric evolution law on a given two dimensional manifold which is embedded or immersed in the three-dimensional Euclidean space. We derive a system of…
We analyze the anisotropy of turbulence in an electrically conducting fluid in the presence of a uniform magnetic field, for low magnetic Reynolds number, using the quasi-static approximation. In the linear limit, the kinetic energy of…
A theoretical analysis is carried out to study flow evolution inside the laminar Rayleigh-B\'enard convection system laden with small particles. By describing particle dynamics and particle heat as sources of drag and heat respectively, the…
The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the relationship for the energy variation, work done,…
We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its…
A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field $\bi u$ and the lattice velocity ${\bi v}=\p {\bi u}/\p t$. Damping is…
This paper deals with a generalized length-preserving flow for convex curves in the plane. It is shown that the flow exists globally and deforms convex curves into circles as time tends to infinity.
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
The $p$-Laplacian evolution equation in metric measure spaces has been studied as the gradient flow in $L^2$ of the $p$-Cheeger energy (for $1 < p < \infty$). In this paper, using the first-order differential structure on a metric measure…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model…
A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of…
We study the behavior of a tracer particle driven by a one-dimensional fluctuating potential, defined initially as a Brownian motion, and evolving in time according to the heat equation. We obtain two main results. First, in the short time…
In this paper we give rates of convergence for the $p$-curve shortening flow for $p\geq 1$ an integer, which improves on the known estimates and which are probably sharp.
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…
In this paper we study a flow by minkowskian curvature where we have a different Minkowski plane at each time. We derive some evolution formulas, present sufficient hypotesis for the short time existence and convexity of solutions and study…