arXiv subjects

Juhyeong Lee

Publications and source records attributed to Juhyeong Lee.

5 recordsLinked to original sources

arXiv2026

Geometric refinements of Liouville-type theorems for the stationary Navier--Stokes equations in $\mathbb{R}^3$

We prove Liouville-type theorems for smooth solutions $(u,p)$ of the stationary Navier--Stokes equations in $\mathbb R^3$ satisfying the finite Dirichlet energy condition and the uniform decay condition. Our results give geometric refinements of two recent Osgood-type criteria, namely the relative decay criterion and the weighted integrability criterion formulated in terms of the head pressure $Q=\frac{1}{2}|u|^2+p$. The proof exploits several properties of the head pressure and the scalar triple-product structure of $(u\timesω)\cdot\nabla Q$. Combined with an Osgood-type representation of the total vorticity energy, this geometric structure yields Liouville-type criteria involving only the tangential interaction of $u$ and $ω$ over the superlevel sets of $|Q|$. In the relative decay setting, they lead to Osgood-scale smallness conditions that allow subcritical growth beyond the corresponding uniform bounds. In the weighted integrability setting, the previous conditions involving the full velocity and velocity gradient are refined to involve only the tangential components of $u$ and $ω$ along the level surfaces of $Q$, together with an angular factor measuring their relative orientation.

math.AP↗

arXiv2026

Liouville-type theorems for the stationary fractional Navier-Stokes equations in $\mathbb{R}^n$

We establish Liouville-type theorems for the stationary fractional Navier-Stokes equations in $\mathbb{R}^n$ under suitable integrability conditions on the velocity field $u$ and a large-scale Morrey-type bound on the fractional energy. As a corollary, these assumptions are automatically satisfied if $u \in \dot{H}^{\fracα{2}}(\mathbb{R}^n)$, yielding Liouville-type results under the finite fractional energy condition for $\frac{n}{3} \le α< \frac{n+2}{3}$, where $α$ denotes the order of the fractional Laplacian $(-Δ)^{\fracα{2}}$. This range reflects a scaling-critical correspondence between Liouville-type theorems in the finite-energy setting and the threshold arising in partial regularity theory. The proof relies on direct kernel estimates for the commutator of the fractional Laplacian, based on a dyadic decomposition of the tail term, which remain valid in the hyper-dissipative case. The argument also uses a bootstrap argument that propagates integrability from near the scaling-invariant exponent down to lower exponents, including the Sobolev embedding exponent.

math.AP↗

arXiv2023

Residual-based physics-informed transfer learning: A hybrid method for accelerating long-term CFD simulations via deep learning

While a big wave of artificial intelligence (AI) has propagated to the field of computational fluid dynamics (CFD) acceleration studies, recent research has highlighted that the development of AI techniques that reconciles the following goals remains our primary task: (1) accurate prediction of unseen (future) time series in long-term CFD simulations (2) acceleration of simulations (3) an acceptable amount of training data and time (4) within a multiple PDEs condition. In this study, we propose a residual-based physics-informed transfer learning (RePIT) strategy to achieve these four objectives using ML-CFD hybrid computation. Our hypothesis is that long-term CFD simulation is feasible with the hybrid method where CFD and AI alternately calculate time series while monitoring the first principle's residuals. The feasibility of RePIT strategy was verified through a CFD case study on natural convection. In a single training approach, a residual scale change occurred around 100th timestep, resulting in predicted time series exhibiting non-physical patterns as well as a significant deviations from the ground truth. Conversely, RePIT strategy maintained the residuals within the defined range and demonstrated good accuracy throughout the entire simulation period. The maximum error from the ground truth was below 0.4 K for temperature and 0.024 m/s for x-axis velocity. Furthermore, the average time for 1 timestep by the ML-GPU and CFD-CPU calculations was 0.171 s and 0.015 s, respectively. Including the parameter-updating time, the simulation was accelerated by a factor of 1.9. In conclusion, our RePIT strategy is a promising technique to reduce the cost of CFD simulations in industry. However, more vigorous optimization and improvement studies are still necessary.

physics.flu-dyn↗

arXiv2023

Finite volume method network for acceleration of unsteady computational fluid dynamics: non-reacting and reacting flows

Despite rapid improvements in the performance of central processing unit (CPU), the calculation cost of simulating chemically reacting flow using CFD remains infeasible in many cases. The application of the convolutional neural networks (CNNs) specialized in image processing in flow field prediction has been studied, but the need to develop a neural netweork design fitted for CFD is recently emerged. In this study, a neural network model introducing the finite volume method (FVM) with a unique network architecture and physics-informed loss function was developed to accelerate CFD simulations. The developed network model, considering the nature of the CFD flow field where the identical governing equations are applied to all grids, can predict the future fields with only two previous fields unlike the CNNs requiring many field images (>10,000). The performance of this baseline model was evaluated using CFD time series data from non-reacting flow and reacting flow simulation; counterflow and hydrogen flame with 20 detailed chemistries. Consequently, we demonstrated that (1) the FVM-based network architecture provided improved accuracy of multistep time series prediction compared to the previous MLP model (2) the physic-informed loss function prevented non-physical overfitting problem and ultimately reduced the error in time series prediction (3) observing the calculated residuals in an unsupervised manner could indirectly estimate the network accuracy. Additionally, under the reacting flow dataset, the computational speed of this network model was measured to be about 10 times faster than that of the CFD solver.

cs.LG↗

arXiv2018

Investigating the Composite/Metal Interface and its Influence on the Electrical Resistance Measurement

The advantages introduced by carbon fiber reinforced polymer (CFRP) composites has made them an appropriate choice in many applications and an ideal replacement for conventional materials. The benefits using CFRP composites are due to their lightweight, high stiffness, as well as corrosion resistance. For this reason, there is a fast growing trend in using CFRP composites for aircraft and wind turbine structural applications. The replacement of the conventional aerospace-grade metal alloys (aluminum, titanium, magnesium, etc.) with CFRP composites results in new challenges. For example, an aircraft during flight is prone to be struck by lightning. To withstand the injection of such massive amount of energy, adequate electrical properties, mainly electrical conductivity, is required. In fact, electrical conductance (or its reciprocal, resistance) is a critical parameter representing any material change and it can be considered an index for health monitoring. In this paper, AS4/8552 carbon/epoxy laminated composites were injected with two types of electrical currents, impulse current and direct current. The change in measured electrical resistance was recorded. A significant resistance drop occurred after electrical current injections. Furthermore, four-point flexural tests were performed on these composites to correlate an electrical resistance change with a potential flexural property change. There was no clear trend between a resistance change and flexural strength/modulus change of the test coupons, regardless of current injection. However, it was observed that the injection of the current affects the contact resistance such that its resistance decreases.

physics.app-ph↗