Critical functional framework and maximal regularity in action on systems of incompressible flows

Abstract. Application of the Brown-Samelson theorem, which shows that particle motion is integrable in a class of vorticity-conserving, two-dimensional incompressible flows, is extended here to a class of explicit time dependent dynamically balanced flows in multilayered systems. Particle motion for nonsteady two-dimensional flows with discontinuities in the vorticity or potential vorticity fields (modon solutions) is shown to be integrable. An example of a two-layer modon solution constrained by observations of a Gulf Stream ring system is discussed.

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Lattice-BGK Methods for Simulating Incompressible Fluid Flows

International Journal of Modern Physics C ◽

10.1142/s0129183197000680 ◽

1997 ◽

Vol 08 (04) ◽

pp. 793-803 ◽

Cited By ~ 10

Author(s):

Yu Chen ◽

Hirotada Ohashi

Keyword(s):

Fluid Flow ◽

Incompressible Fluid ◽

Poisson Equation ◽

General Model ◽

Incompressible Flows ◽

Fluid Flows ◽

Incompressible Limit ◽

Numerical Example ◽

Incompressible Fluid Flows

The lattice-Bhatnagar-Gross-Krook (BGK) method has been used to simulate fluid flow in the nearly incompressible limit. But for the completely incompressible flows, two special approaches should be applied to the general model, for the steady and unsteady cases, respectively. Introduced by Zou et al.,1 the method for steady incompressible flows will be described briefly in this paper. For the unsteady case, we will show, using a simple numerical example, the need to solve a Poisson equation for pressure.

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$L^{p}-L^{q}$-Maximal regularity of the Van Wijngaarden–Eringen equation in a cylindrical domain

Advances in Difference Equations ◽

10.1186/s13662-020-03054-5 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Carlos Lizama ◽

Marina Murillo-Arcila

Keyword(s):

Acoustic Waves ◽

Maximal Regularity ◽

Bubble Radius ◽

Fourier Multipliers ◽

Cylindrical Domain ◽

Lebesgue Spaces ◽

Regularity Problem ◽

Bubbly Liquids

Abstract We consider the maximal regularity problem for a PDE of linear acoustics, named the Van Wijngaarden–Eringen equation, that models the propagation of linear acoustic waves in isothermal bubbly liquids, wherein the bubbles are of uniform radius. If the dimensionless bubble radius is greater than one, we prove that the inhomogeneous version of the Van Wijngaarden–Eringen equation, in a cylindrical domain, admits maximal regularity in Lebesgue spaces. Our methods are based on the theory of operator-valued Fourier multipliers.

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