Related papers: An inverse source problem for convective Brinkman-…
In this article, we study an inverse problem for the following convective Brinkman-Forchheimer (CBF) equations: \begin{align*} \boldsymbol{u}_t-\mu…
In this article, we study an inverse problem for the following convective Brinkman-Forchheimer (CBF) equations: \begin{align*} \boldsymbol{u}_t-\mu…
The following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) with potential \begin{equation*} \frac{\partial \boldsymbol{y}}{\partial t}-\mu…
In this work, we consider the two- and three-dimensional convective Brinkman-Forchheimer (CBF) equations (or damped Navier--Stokes equations) on a torus $\mathbb{T}^d,$ $d\in\{2,3\}$: $$ \frac{\partial \boldsymbol{u}}{\partial t}-\mu…
The convective Brinkman--Forchheimer equations or the Navier--Stokes equations with damping in bounded or periodic domains $\subset\mathbb{R}^d$, $2\leq d\leq 4$ are considered in this work. The existence and uniqueness of a global weak…
It has been pointed out in the work [F. Gozzi et.al., \emph{Arch. Ration. Mech. Anal.} {163}(4) (2002), 295--327] that the existence and uniqueness of viscosity solutions to the first-order Hamilton-Jacobi-Bellman equation (HJBE) associated…
In this article, we discuss the local exact controllability to trajectories of the following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) defined in a bounded domain $\Omega \subset\mathbb{R}^d$…
In this work, we consider the following two- and three-dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations in torus $\mathbb{T}^d,\ d\in\{2,3\}$: \begin{align*} \mathrm{d}\boldsymbol{u}+\left[-\mu…
In this work, we analyze the long time behavior of 2D as well as 3D convective Brinkman-Forchheimer (CBF) equations and its stochastic counter part with non-autonomous deterministic forcing term in $\mathbb{R}^d$ $ (d=2, 3)$:…
In this paper we give a simple proof of the existence of global-in-time smooth solutions for the convective Brinkman-Forchheimer equations (also called in the literature the tamed Navier-Stokes equations) $$ \partial_tu -\mu\Delta u + (u…
In this work, we investigate the existence and uniqueness of solutions to the following 2D and 3D convective Brinkman-Forchheimer extended Darcy equations defined on a bounded smooth domain $\Omega\subset\mathbb{R}^d$, $d\in\{2,3\}$,…
The convective Brinkman-Forchheimer equations (CBFEs) \[ \frac{\partial \boldsymbol{X}}{\partial t} - \mu \Delta\boldsymbol{X} + (\boldsymbol{X}\cdot\nabla)\boldsymbol{X} + \alpha\boldsymbol{X} + \beta|\boldsymbol{X}|^{r-1}\boldsymbol{X} +…
The flow of incompressible fluid in highly permeable porous media in vorticity - velocity - Bernoulli pressure form leads to a double saddle-point problem in the Navier--Stokes--Brinkman--Forchheimer equations. The paper establishes, for…
In this work, we consider the following 2D stochastic convective Brinkman-Forchheimer (SCBF) equations in a bounded smooth domain $\mathcal{O}$: \begin{align*} \mathrm{d}\boldsymbol{u}+\left[-\mu…
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…
The stochastic convective Brinkman-Forchheimer (SCBF) equations in an open connected set $\mathcal{O}\subseteq\mathbb{R}^d$ ($d\in \{2,3,4\}$) or torus are considered in this work. We show the existence of a pathwise unique strong solution…
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…
This article develops the viscosity solution approach to the large deviation principle for the following two- and three-dimensional stochastic convective Brinkman-Forchheimer equations on the torus $\mathbb{T}^d,\ d\in\{2,3\}$ with small…
In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…
In this paper, we study an inverse problem of identifying two spatial-temporal source terms in the Schr\"odinger equation with dynamic boundary conditions from the final time overdetermination. We adopt a weak solution approach to solve the…