Maximal regularity for gradient systems with boundary degeneracy

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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Stabilization of the chemotaxis–Navier–Stokes equations: maximal regularity approach

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125422 ◽

2021 ◽

pp. 125422

Author(s):

Keiichi Watanabe

Keyword(s):

Maximal Regularity ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations

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Lorentz spaces in action on pressureless systems arising from models of collective behavior

Journal of Evolution Equations ◽

10.1007/s00028-021-00668-4 ◽

2021 ◽

Author(s):

Raphaël Danchin ◽

Piotr Bogusław Mucha ◽

Patrick Tolksdorf

Keyword(s):

Initial Data ◽

Collective Behavior ◽

Existence And Uniqueness ◽

Maximal Regularity ◽

Parabolic Systems ◽

Lorentz Spaces ◽

Regularity Estimate ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Time Existence

AbstractWe are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in $$L_{q,r}(0,T;L_p(\Omega ))$$ L q , r ( 0 , T ; L p ( Ω ) ) spaces.

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STARCH GEL ELECTROPHORESIS OF MYOGEN FROM CHICKEN BREAST MUSCLE IN CONSTANT AND GRADIENT BUFFER SYSTEMS

Canadian Journal of Biochemistry and Physiology ◽

10.1139/y63-046 ◽

1963 ◽

Vol 41 (1) ◽

pp. 369-387 ◽

Cited By ~ 4

Author(s):

J. M. Neelin

Keyword(s):

Gel Electrophoresis ◽

Protein Concentration ◽

Breast Muscle ◽

Chicken Breast ◽

Starch Gel Electrophoresis ◽

Two Dimensional ◽

Sodium Cacodylate ◽

Gradient Systems ◽

Optimal Separation ◽

Starch Gel

By varying conditions of starch gel electrophoresis, factors contributing to the resolution of myogen proteins from chicken breast muscle have been studied. Variables examined included composition of the myogen extractant, protein concentration, ionic strength of electrophoretic media, pH of gel media, plane and direction of electrophoresis, and the nature of cations and anions in gel media and bridge solutions. The significance of anions was more closely studied with constant buffer systems, and gradient systems in which bridge electrolyte differed from, and gradually altered, the gel medium. Optimal separation was obtained in gradient systems with 0.10 M sodium chloride bridge solutions, and gel media of sodium cacodylate, pH 6.9, μ 0.010, which resolved 12 cationic zones, and sodium veronal, pH 7.4, μ 0.010, which resolved 10 anionic zones. These buffers in two-dimensional sequence revealed a total of about 24 components in this myogen.

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