The Legacy of Roland Glowinski by Bensoussan, Alain, Pironneau, Olivier

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Evolution of CFD numerical methods and physical models towards a full discrete approach by Caltagirone, Jean-Paul

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A Navier–Stokes-Informed Neural Network for Simulating the Flow Behavior of Flowable Cement Paste in 3D Concrete Printing by Tianjie Zhang, Donglei Wang, Yang Lu

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Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media by Kuan, Jeffrey, Čanić, Sunčica, Muha, Boris

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Navier-Stokes: Singularities and Bifurcations by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales

“… This article presents substantial advances in the analysis of the Navier-Stokes equations for both compressible and incompressible fluids, focusing on the formation of singularities, hypercomplex bifurcations, and regularity in Sobolev and Besov spaces. …”
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Turbulent Flow Analysis with Banach and Sobolev Spaces in the LES Method Incorporating the Smagorinsky Subgrid-Scale Model by Rômulo Damasclin Chaves dos Santos, Jorge Henrique Oliveira Sales

“…At first, the effort dedicated here aims to present a more comprehensive mathematical analysis, promoting a more leveled understanding of the challenge posed by the regularity of the Navier-Stokes equations. …”
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Classical Solvability of a Free Boundary Problem for an Incompressible Viscous Fluid with a Surface Density Equation by Yoshiaki Kusaka

“…The model is described as a free boundary problem consisting of the Navier-Stokes equations and a surface mass balance equation. …”
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Algebra Properties in Fourier-Besov Spaces and Their Applications by Xuhuan Zhou, Weiliang Xiao

“…As applications of these algebra properties, we establish the global well-posedness for small initial data and local well-posedness for large initial data of the generalized Navier-Stokes equations. Particularly, we give a blow-up criterion of the solutions in Fourier-Besov spaces as well as a space analyticity of Gevrey regularity.…”
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On the Nusselt Solution of a Nonisothermal Two-Fluid Inclined Film Flow by Jürgen Socolowsky

“…The corresponding mathematical models often represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In the present paper we are concerned with a particular problem of coupled heat and mass transfer. …”
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Global Existence for the 3D Tropical Climate Model with Small Initial Data in H˙1/2ℝ3∗ by Hui Zhang, Juan Xu

“…This result can be regard as a generalization of the famous Fujita–Kato result to 3D Navier–Stokes equations.…”
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Sensitivity Analysis of Transonic Flow over J-78 Wings by Alexander Kuzmin

“…Solutions of the unsteady Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver on unstructured meshes. …”
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Global Well-Posedness and Large-Time Behavior for the Equilibrium Diffusion Model in Radiation Hydrodynamics by Peng Jiang, Jinkai Ni, Lu Zhu

“…The model consists of the compressible Navier-Stokes equations coupled with radiation effect terms described by the fourth power of temperature. …”
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Conservation Laws for Some Systems of Nonlinear Partial Differential Equations via Multiplier Approach by Rehana Naz

“…The conservation laws for the integrable coupled KDV type system, complexly coupled kdv system, coupled system arising from complex-valued KDV in magnetized plasma, Ito integrable system, and Navier stokes equations of gas dynamics are computed by multipliers approach. …”
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Nanofluidics and Nanofluids Shape Oscillation of a Single Microbubble in an Ultrasound Field by Xian Li, Fubing Bao, Yuebing Wang

“…The shape oscillation of a single two-dimensional nitrogen microbubble in an ultrasound field is numerically investigated. The Navier–Stokes equations are solved by using the finite-volume method combined with the volume-of-fluid model. …”
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Analytical Equations for Thermoacoustic Instability Sources and Acoustic Radiation from Reacting Turbulence by S. A. E. Miller

“…We present a new theory based on the decomposition of the Navier-Stokes equations coupled with the mass fraction equations. …”
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Stability Analysis of Symmetrical Rotors Partially Filled with a Viscous Incompressible Fluid by Zhu Changsheng

“…On the basis of the linearized fluid forces acting on the rotor obtained directly by using the two-dimensional Navier-Stokes equations, the stability of symmetrical rotors with a cylindrical chamber partially filled with a viscous incompressible fluid is investigated in this paper. …”
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Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation by Mohamed A. El-Beltagy, Mohamed I. Wafa

“…A two-dimensional stochastic solver for the incompressible Navier-Stokes equations is developed. The vorticity-stream function formulation is considered. …”
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Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations by Jae-Hong Pyo

“…The stabilized Gauge-Uzawa method (SGUM), which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. …”
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Numerical Simulation of Combustion and Rotor-Stator Interaction in a Turbine Combustor by Dragos D. Isvoranu, Paul G. A. Cizmas

“…The flow and combustion are modeled by the Reynolds-averaged Navier-Stokes equations coupled with the species-conservation equations. …”
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Large Scale Simulation of Hydrogen Dispersion by a Stabilized Balancing Domain Decomposition Method by Qing-He Yao, Xin Pan

“…The linear systems of Navier-Stokes equations and the convection diffusion equation are symmetrized by a pressure stabilized Lagrange-Galerkin method, and thus a balancing domain decomposition method is enabled to solve the interface problem of the domain decomposition system. …”
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