scholarly journals A model for suspension of clusters of particle pairs

2020 ◽  
Vol 54 (5) ◽  
pp. 1597-1634
Author(s):  
Amina Mecherbet
Keyword(s):  
Existence And Uniqueness ◽  
Additional Assumption ◽  
Local Existence ◽  
Uniqueness Result ◽  
Minimal Distance ◽  
Rigid Spheres ◽  
Limit Model ◽  
Local Existence And Uniqueness ◽  
Particle Pairs ◽  
Mesoscopic Level

In this paper, we consider N clusters of pairs of particles sedimenting in a viscous fluid. The particles are assumed to be rigid spheres and inertia of both particles and fluid are neglected. The distance between each two particles forming the cluster is comparable to their radii 1/N while the minimal distance between the pairs is of order N−1/2. We show that, at the mesoscopic level, the dynamics are modelled using a transport-Stokes equation describing the time evolution of the position x and orientation ξ of the clusters. Under the additional assumption that the minimal distance is of order N−1/3, we investigate the case where the orientation of each cluster is initially correlated to its position. In this case, a local existence and uniqueness result for the limit model is provided.

scholarly journals An Euler-Poisson system in plasmas

2000 ◽  
Vol 41 (4) ◽  
pp. 442-450 ◽  
Author(s):  
A. Nouri
Keyword(s):  
Plasma Physics ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Three Dimensional ◽  
Uniqueness Result ◽  
Poisson System ◽  
Local Existence And Uniqueness ◽  
Pressure Term

AbstractA local existence and uniqueness result is proved for the three-dimensional Euler-Poisson system without a pressure term which arises in plasma physics.

scholarly journals Local and Global Existence of Solution for Love Type Waves with Past History

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1998
Author(s):  
Mohamed Biomy ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Existence And Uniqueness ◽  
Past History ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linearization Method ◽  
Weak Compactness ◽  
Existence Of Solution ◽  
Local Existence And Uniqueness ◽  
Initial Boundary Value

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness of weak solution is proved. Using the potential well method, it is shown that the solution for a class of Love-equation exists globally under some conditions on the initial datum and kernel function.

GENESIS OF A SOURCE/SINK LINE INTO A SINGULAR UPDRAFT

1998 ◽  
Vol 08 (03) ◽  
pp. 431-444 ◽  
Author(s):  
JOËL CHASKALOVIC
Keyword(s):  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Vortex Line ◽  
Stokes Equations ◽  
Local Existence ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Local Existence And Uniqueness ◽  
Source Sink

Mathematical models applied to tornadoes describe these kinds of flows as an axisymmetric fluid motion which is restricted for not developing a source or a sink near the vortex line. Here, we propose the genesis of a family of a source/sink line into a singular updraft which can modeled one of the step of the genesis of a tornado. This model consists of a three-parameter family of fluid motions, satisfying the steady and incompressible Navier–Stokes equations, which vanish at the ground. We establish the local existence and uniqueness for these fields, at the neighborhood of a nonrotating singular updraft.

scholarly journals ROUGH VOLTERRA EQUATIONS 1: THE ALGEBRAIC INTEGRATION SETTING

2009 ◽  
Vol 09 (03) ◽  
pp. 437-477 ◽  
Author(s):  
AURÉLIEN DEYA ◽  
SAMY TINDEL
Keyword(s):  
Brownian Motion ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Volterra Equations ◽  
Existence And Uniqueness Theorem ◽  
Hölder Exponent ◽  
Local Existence And Uniqueness ◽  
Hurst Coefficient ◽  
Rough Path ◽  
Driving Signal

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with Hölder exponent γ > 1/2, we obtain a global solution, and are able to handle the case of a singular Volterra coefficient. In case of a driving signal with Hölder exponent 1/3 < γ < 1/2, we get a local existence and uniqueness theorem. The results are easily applied to the fractional Brownian motion with Hurst coefficient H > 1/3.

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