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Generalizations of incompressible and compressible Navier–Stokes equations to fractional time and multi-fractional space [PDF]
Scientific Reports, 2022 This study develops the governing equations of unsteady multi-dimensional incompressible and compressible flow in fractional time and multi-fractional space. When their fractional powers in time and in multi-fractional space are specified to unit integer
M. Levent Kavvas, Ali Ercan
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Navier-Stokes Equations with Potentials
Abstract and Applied Analysis, 2007 We study Navier-Stokes equations perturbed with a maximal monotone operator, in a bounded domain, in 2D and 3D. Using the theory of nonlinear semigroups, we prove existence results for strong and weak solutions. Examples are also provided.
Adriana-Ioana Lefter
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Energy equality in the isentropic compressible Navier-Stokes-Maxwell equations
Electronic Research Archive, 2023 This paper concerns energy conservation for weak solutions of compressible Navier-Stokes-Maxwell equations. For the energy equality to hold, we provide sufficient conditions on the regularity of weak solutions, even for solutions that may include exist ...
Jie Zhang , Gaoli Huang, Fan Wu
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Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2022 In this paper, we prove the global existence and uniqueness of the weak solutions to the inviscid velocity-vorticity model of the g-Navier-Stokes equations.
Meryem Kaya, Özge Kazar
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Error estimates for physics informed neural networks approximating the Navier-Stokes equations [PDF]
arXiv.org, 2022 We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier-Stokes equations with (extended) physics informed neural networks. We show that the underlying PDE residual can be made arbitrarily small for tanh neural
T. D. Ryck +2 more
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Analytical Solution to 1D Compressible Navier-Stokes Equations
Journal of Function Spaces, 2021 There exist complex behavior of the solution to the 1D compressible Navier-Stokes equations in half space. We find an interesting phenomenon on the solution to 1D compressible isentropic Navier-Stokes equations with constant viscosity coefficient on x,t ...
Changsheng Dou, Zishu Zhao
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Non-uniqueness of Leray solutions of the forced Navier-Stokes equations [PDF]
Annals of Mathematics, 2021 In the seminal work [39], Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. We exhibit two distinct Leray solutions with zero initial velocity and identical body force.
D. Albritton, Elia Bru'e, Maria Colombo
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Physics-informed neural networks for solving Reynolds-averaged Navier-Stokes equations [PDF]
The Physics of Fluids, 2021 Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs).
Hamidreza Eivazi +3 more
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Boundary Value Problems, 2020 In this paper, we consider the three-dimensional compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition in a bounded smooth domain.
Dandan Ren, Yunting Ding, Xinfeng Liang
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