6 citations · 6 across the 5 of their papers we have counts for
8 papers
Error Estimates in Physics-Informed Neural Networks to Heat-Wave Fluid-Structure Interactive System
Pelin G. Geredeli, Mohammad Mahabubur Rahman, Deepanshu Verma
We study a physics-informed neural network (PINN) approximation of a coupled PDE system that models the interaction between fluid and elastic dynamics. The canonical heat-wave mode…
Stochastic Two-Dimensional Anisotropic Magnetohydrodynamics System with Multiplicative Noise
Mohammad Mahabubur Rahman
In this paper, we investigate the stochastic two-dimensional anisotropic magnetohydrodynamics system on with velocity dissipation acting only in the horizontal direct…
Existence of Weak Solutions and Higher-Order Regularity for a Heat-Wave Fluid-Structure Interaction System on a Periodic Strip
Mohammad Mahabubur Rahman
In this paper, we study a heat-wave fluid-structure interaction system posed on a periodic strip geometry and investigate whether higher-order -estimates for arbitrarily large…
Regularity and error estimates in physics-informed neural networks for the Kuramoto-Sivashinsky equation
Mohammad Mahabubur Rahman, Deepanshu Verma
Due to its nonlinearity, bi-harmonic dissipation, and backward heat-like term in the absence of a divergence-free condition, the -D/-D Kuramoto-Sivashinsky equation poses sig…
Analysis and Numerical Approximation to Interactive Dynamics of Navier Stokes-Plate Interaction PDE System
Pelin G. Geredeli, Quyuan Lin, Dylan Mcknight +1
We consider a Navier-Stokes fluid-plate interaction (FSI) system which describes the evolutions of the fluid contained within a 3D cavity, as it interacts with a deformable elastic…
Another remark on the global regularity issue of the Hall-magnetohydrodynamics system
Mohammad Mahabubur Rahman, Kazuo Yamazaki
We discover cancellations upon -estimate of the Hall term for . As its consequence, first, we derive a regularity criterion for the 3-dimensio…
Remarks on the global regularity issue of the two and a half dimensional Hall-magnetohydrodynamics system
Mohammad Mahabubur Rahman, Kazuo Yamazaki
Whether or not the solution to the -dimensional Hall-magnetohydrodynamics system starting from smooth initial data preserves its regularity for all time remains a cha…
Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three
Adam Larios, Mohammad Mahabubur Rahman, Kazuo Yamazaki
We propose and prove several regularity criteria for the 2D and 3D Kuramoto-Sivashinsky equation, in both its scalar and vector forms. In particular, we examine integrability crite…