A high‐order stabilized solver for the volume averaged Navier‐Stokes equations
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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
Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D
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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
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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
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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
Global regularity criterion for the Navier‐Stokes equations based on the direction of vorticity
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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
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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
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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
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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
The Inviscid Limit of Navier–Stokes Equations for Analytic Data on the Half-Space
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DOI: 10.1007/s00205-018-1266-9
Abstract: In their classical work, Sammartino and Caflisch (Commun Math Phys 192(2):433–461, 1998a; Commun Math Phys 192(2):463–491, 1998b) proved the inviscid limit of the incompressible Navier–Stokes equations for well-prepared data with analytic regularity in the half-space.… read more here.
Keywords: inviscid limit; analytic data; stokes equations; limit ... See more keywords
Stationary Solutions and Nonuniqueness of Weak Solutions for the Navier–Stokes Equations in High Dimensions
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DOI: 10.1007/s00205-019-01366-9
Abstract: Consider the unforced incompressible homogeneous Navier–Stokes equations on the d-torus $${\mathbb{T}^d}$$Td where $${d \geq 4}$$d≥4 is the space dimension. It is shown that there exist nontrivial steady-state weak solutions $${u \in L^{2} (\mathbb{T}^d)}$$u∈L2(Td). The result… read more here.
Keywords: stationary solutions; stokes equations; weak solutions; solutions nonuniqueness ... See more keywords
The Inviscid Limit for the Navier–Stokes Equations with Data Analytic Only Near the Boundary
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DOI: 10.1007/s00205-020-01517-3
Abstract: We address the inviscid limit for the Navier–Stokes equations in a half space, with initial datum that is analytic only close to the boundary of the domain, and that has Sobolev regularity in the complement.… read more here.
Keywords: inviscid limit; limit navier; stokes equations; equations data ... See more keywords