arXiv subjects

Jyoti Jindal

Publications and source records attributed to Jyoti Jindal.

3 recordsLinked to original sources

arXiv2026

A Quasi-Variational--Hemivariational Inequality for the Convective Brinkman--Forchheimer Extended Darcy Equations with Bingham Fluids

This paper is devoted to the analysis of a quasi-variational--hemivariational inequality associated with the convective Brinkman--Forchheimer extended Darcy (CBFeD) equations for Bingham fluids in both two and three spatial dimensions. The considered model describes incompressible fluid flow through porous media while incorporating convection, nonlinear damping effects, and Forchheimer-type resistance, together with non-smooth and non-convex slip boundary conditions. We first derive an appropriate weak formulation of the problem, which leads naturally to a Bingham-type quasi-variational--hemivariational inequality with a velocity-dependent constraint set. By employing the Kakutani--Ky Fan fixed point theorem, we establish the existence of weak solutions for the resulting multivalued quasi-variational inequality formulation of the CBFeD system. Furthermore, we prove that every weak solution of the associated quasi-variational inequality is also a solution of the corresponding quasi-variational--hemivariational inequality. The analysis presented in this work provides a rigorous mathematical framework for CBFeD models with Bingham fluids under non-monotone and non-smooth boundary interactions.

math.AP↗

arXiv2026

A domain hemivariational inequality for 2D and 3D convective Brinkman-Forchheimer extended Darcy equations

This paper investigates domain hemivariational inequality problems arising from the non-stationary two- and three-dimensional convective Brinkman-Forchheimer extended Darcy (CBFeD) equations, which describe the flow of viscous incompressible fluids through saturated porous media in bounded domains. These equations may be regarded as generalized Navier-Stokes systems incorporating both damping and pumping mechanisms. For all admissible absorption exponents $r \ge 1 $ and effective viscosity $\mu > 0 $, the existence of weak solutions to the non-stationary 2D and 3D CBFeD equations with hemivariational inequalities is established via a regularized Galerkin approximation scheme, based on a suitable regularization of the Clarke subdifferential. A noteworthy aspect of the analysis is that the existence results extend to the three-dimensional non-stationary Navier-Stokes equations. Moreover, under appropriate conditions on the absorption exponent, specifically, $r \ge 1 $ in two dimensions and $ r \ge 3 $ in three dimensions, it is shown that weak solutions satisfy the energy equality. In addition, uniqueness of solutions is proved for $ r \ge 1$ in 2D and $r \ge 3$ in 3D, with the additional requirement $2\beta \mu > 1 $ in the critical case $r = 3 $.

math.AP↗

arXiv2025

Well-posedness of a boundary hemivariational inequality for stationary and non-stationary 2D and 3D convective Brinkman-Forchheimer equations

This paper investigates boundary hemivariational inequality problems associated with both stationary and non-stationary two and three-dimensional convective Brinkman-Forchheimer equations (or Navier-stokes equations with damping), which model the flow of viscous incompressible fluids through saturated porous media. The governing equations are nonlinear in both velocity and pressure and are subject to nonstandard boundary conditions. Specifically, we impose the no-slip condition along with a Clarke subdifferential relation between pressure and the normal velocity components. For the stationary case, we establish the existence and uniqueness of weak solutions using a surjectivity theorem for pseudomonotone operators. The existence of weak solutions to the non-stationary hemivariational inequality is established via a limiting process applied to a temporally semi-discrete scheme, where the time derivative is approximated using the backward Euler method-commonly referred to as the Rothe method. It is demonstrated that the discrete problem admits solutions, which possess a weakly convergent subsequence as the time step tends to zero, and that any such weak limit satisfies the original hemivariational inequality. A novel outcome of this paper is that the existence results obtained in this work is applicable to 3D non-stationary Navier-Stokes equations also. Moreover, under appropriate conditions on the absorption exponent, we show that Leray-Hopf weak solutions satisfies the energy equality, the solution is shown to be unique and to depend continuously on the given data.

math.AP↗