Quantitative Regularity Estimates for Compressible Transport Equations

2018 ◽  
pp. 77-113 ◽  
Author(s):  
Didier Bresch ◽  
Pierre-Emmanuel Jabin
Keyword(s):  
Transport Equations ◽  
Regularity Estimates ◽  
Quantitative Regularity

scholarly journals Space regularity for evolution operators modeled on Hörmander vector fields with time dependent measurable coefficients

2020 ◽  
Author(s):  
Marco Bramanti
Keyword(s):  
Vector Fields ◽  
Evolution Operators ◽  
Invariant Vector ◽  
Measurable Coefficients ◽  
Regularity Estimates ◽  
Hörmander Vector Fields ◽  
Derivatives Of ◽  
Homogeneous Vector Fields ◽  
Quantitative Regularity ◽  
Continuity Estimate

Abstract We consider a heat-type operator $$\mathcal {L}$$ L structured on the left invariant 1-homogeneous vector fields which are generators of a Carnot group, with a uniformly positive matrix of bounded measurable coefficients depending only on time. We prove that if $$\mathcal {L}u$$ L u is smooth with respect to the space variables, the same is true for u, with quantitative regularity estimates in the scale of Sobolev spaces defined by right invariant vector fields. Moreover, the solution and its space derivatives of every order satisfy a 1/2-Hölder continuity estimate with respect to time. The result is proved both for weak solutions and for distributional solutions, in a suitable sense.

Maxwell’s Equations versus Newton’s Third Law

2018 ◽  
Author(s):  
Glyn Kennell ◽  
Richard Evitts
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Simulated Data ◽  
Numerical Data ◽  
Transport Equations ◽  
Concentration Gradients ◽  
Third Law

The presented simulated data compares concentration gradients and electric fields with experimental and numerical data of others. This data is simulated for cases involving liquid junctions and electrolytic transport. The objective of presenting this data is to support a model and theory. This theory demonstrates the incompatibility between conventional electrostatics inherent in Maxwell's equations with conventional transport equations. <br>

Sediment transport over fixed deposited beds in sewers - An appraisal of existing models

1997 ◽  
Vol 36 (8-9) ◽  
pp. 123-128 ◽  
Author(s):  
C. Nalluri ◽  
A. K. El-Zaemey ◽  
H. L. Chan
Keyword(s):  
Sediment Transport ◽  
Fixed Bed ◽  
Transport Equations ◽  
Design Criterion ◽  
Pipe Diameter ◽  
Transport Velocity

An appraisal of the existing sediment transport equations was made using May et al (1989) and Ackers (1991) sediment transport equations for the limit of deposition design criterion and with a deposit depth of 1% of the pipe diameter allowed in the sewers. The applicability of those equations for sewers with larger fixed bed deposit depth was assessed, the equations generally over-estimated the transport velocity. Modifications were made to enable the equations to apply to sewers with large fixed bed deposits present.

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