A high‐order stabilized solver for the volume averaged Navier‐Stokes equations
Sign Up to like & getrecommendations! Published in 2022 at "International Journal for Numerical Methods in Fluids"
DOI: 10.1002/fld.5182
Abstract: The volume‐averaged Navier‐Stokes equations are used to study fluid flow in the presence of fixed or moving solids such as packed or fluidized beds. We develop a high‐order finite element solver using both forms A… read more here.
Keywords: solver; volume averaged; averaged navier; order ... See more keywords
Convergence of approximating solutions of the Navier–Stokes equations in higher ordered Sobolev norms
Sign Up to like & getrecommendations! Published in 2025 at "Mathematische Nachrichten"
DOI: 10.1002/mana.12009
Abstract: We show that the approximating solutions {uj}j=0∞$\lbrace u_j\rbrace _{j=0}^{\infty }$ of the Navier–Stokes equations constructed by Kato with the initial data u(0)∈Lσn(Rn)$u(0) \in L_{\sigma }^{n}(\mathbb {R}^{n})$ converge to the local strong solution u$u$ in the… read more here.
Keywords: approximating solutions; mathbb; navier stokes; convergence approximating ... See more keywords
Local existence and nonexistence of fractional Rayleigh–Stokes equations with a superlinear source term
Sign Up to like & getrecommendations! Published in 2025 at "Mathematische Nachrichten"
DOI: 10.1002/mana.12010
Abstract: Fractional Rayleigh–Stokes equations can be described as the viscoelasticity of non‐Newtonian fluids behavior for a generalized second grade fluid. In this paper, we present the monotone iteration method to investigate the nonlinear fractional Rayleigh–Stokes equations… read more here.
Keywords: stokes equations; fractional rayleigh; local existence; rayleigh stokes ... See more keywords
Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201700050
Abstract: We consider Navier-Stokes equations for compressible viscous fluids in one dimension. We prove the existence of global strong solution with large initial data for the shallow water system. The key ingredient of the proof relies… read more here.
Keywords: existence global; strong solution; global strong; stokes equations ... See more keywords
The D incompressible Navier–Stokes equations with partial hyperdissipation
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201700176
Abstract: Funding information NSFC, Grant/Award Numbers: 11601011, 11671273, 11231006; NSF, Grant/Award Number: 1614246 Abstract The three-dimensional incompressible Navier–Stokes equations with the hyperdissipation (−Δ)γ always possess global smooth solutions when γ ≥ 4 . Tao [6] and… read more here.
Keywords: stokes equations; equations partial; incompressible navier; partial hyperdissipation ... See more keywords
Global existence versus blow‐up results for one dimensional compressible Navier–Stokes equations with Maxwell's law
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201700418
Abstract: We consider one dimensional isentropic compressible Navier–Stokes equations with constitutive relation of Maxwell's law instead of Newtonion law. For this new model, we show that for small initial data, a unique smooth solution exists globally… read more here.
Keywords: compressible navier; stokes equations; one dimensional; maxwell law ... See more keywords
Spatially Periodic Solutions for Evolution Anisotropic Variable‐Coefficient Navier–Stokes Equations: II. Serrin‐Type Solutions
Sign Up to like & getrecommendations! Published in 2024 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.10921
Abstract: We consider evolution (nonstationary) space‐periodic solutions to the n$$ n $$ ‐dimensional nonlinear Navier–Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in space and time and satisfying the relaxed ellipticity condition. Employing… read more here.
Keywords: type solutions; navier stokes; stokes equations; periodic solutions ... See more keywords
Global regularity criterion for the Navier‐Stokes equations based on the direction of vorticity
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5818
Abstract: We study the regularity criterion for the Navier‐Stokes equations and show that the (β1,β2,β3)‐Hölder continuity assumption in (x1,x2,x3) on the direction of the vorticity ensures the regularity of the solution. This may be viewed as… read more here.
Keywords: navier stokes; stokes equations; regularity criterion; criterion navier ... See more keywords
Time‐periodic Stokes equations with inhomogeneous Dirichlet boundary conditions in a half‐space
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6048
Abstract: The time‐periodic Stokes problem in a half‐space with fully inhomogeneous right‐hand side is investigated. Maximal regularity in a time‐periodic Lp setting is established. A method based on Fourier multipliers is employed that leads to a… read more here.
Keywords: time; half space; periodic stokes; stokes equations ... See more keywords
The fractal dimension of pullback attractors for the 2D Navier–Stokes equations with delay
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6634
Abstract: This paper is concerned with the bounded fractal and Hausdorff dimension of the pullback attractors for 2D nonautonomous incompressible Navier‐Stokes equations with constant delay terms. Using the construction of trace formula with two bases for… read more here.
Keywords: navier stokes; pullback attractors; dimension pullback; dimension ... See more keywords
Global well‐posedness for the stochastic non‐Newtonian fluid equations and convergence to the Navier‐Stokes equations
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.6827
Abstract: I will deliver my talk in two sessions. The first part contains motivation and preliminaries about stochastic partial differential equations. The existence of global pathwise solutions for the stochastic non-Newtonian incompressible fluid equations in space… read more here.
Keywords: fluid equations; stochastic non; stokes equations; non newtonian ... See more keywords