A dive into the asymptotic analysis theory: a short review from fluids to financial markets

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Fundamental topics (basic mathematics, methodology; applicable to economics in general) (91B02) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) PDEs in connection with biology, chemistry and other natural sciences (35Q92)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Highly rotating viscous compressible fluids in presence of capillarity effects
Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weight
Scale interactions in compressible rotating fluids
A singular limit problem for rotating capillary fluids with variable rotation axis
A new model for self-organized dynamics and its flocking behavior
Multi-scale analysis of compressible viscous and rotating fluids
Multiscale analysis in the compressible rotating and heat conducting fluids
Fast rotation limit for the 2-D non-homogeneous incompressible Euler equations
From particle to kinetic and hydrodynamic descriptions of flocking
Incompressible limit for a viscous compressible fluid
Fokker-Planck equation of distributions of financial returns and power laws
A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment
The Cucker-Smale equation: singular communication weight, measure-valued solutions and weak-atomic uniqueness
Inviscid limit for SQG equation in different dispersive regimes via relative energy inequality
Examples of dispersive effects in non-viscous rotating fluids
Rotating fluids in a cylinder
Relative entropies, suitable weak solutions, and weak-strong uniqueness for the compressible Navier-Stokes system
A multiscale problem for viscous heat-conducting fluids in fast rotation
Rigorous derivation and well-posedness of a quasi-homogeneous ideal MHD system
Incompressible and fast rotation limit for barotropic Navier-Stokes equations at large Mach numbers
Volatility flocking by Cucker-Smale mechanism in financial markets
Long time dynamics of forced critical SQG
Asymptotics of fast rotating density-dependent incompressible fluids in two space dimensions
Derivation of geostrophic equations as a rigorous limit of compressible rotating and heat conducting fluids with the general initial data
A particle model for the herding phenomena induced by dynamic market signals
Inviscid incompressible limits for rotating fluids
Weak convergence results for inhomogeneous rotating fluid equations
Critical thresholds in 1D Euler equations with non-local forces
Multiple Scales and Singular Limits for Compressible Rotating Fluids with General Initial Data
A Singular Limit for Compressible Rotating Fluids
ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES
Critical thresholds in flocking hydrodynamics with non-local alignment
Particle, kinetic, and hydrodynamic models of swarming
Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation
Sociophysics: A new approach of sociological collective behaviour. I. mean‐behaviour description of a strike
Inviscid limits and regularity estimates for the solutions of the 2-D dissipative quasi-geostrophic equations
Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
Vanishing viscosity limits and long-time behavior for 2D quasi-geostrophic equations
Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing
Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives
On the fast rotation asymptotics of a non-homogeneous incompressible MHD system
Hydrodynamic limit of the kinetic Cucker–Smale flocking model
Euler-type equations and commutators in singular and hyperbolic limits of kinetic Cucker–Smale models
Emergent Behavior in Flocks
Singular limits in thermodynamics of viscous fluids
On the analysis of a coupled kinetic-fluid model with local alignment forces
From BGK-alignment model to the pressured Euler-alignment system with singular communication weights
On the influence of gravity in the dynamics of geophysical flows
Fast rotation and inviscid limits for the SQG equation with general ill-prepared initial data

This page was built for publication: A dive into the asymptotic analysis theory: a short review from fluids to financial markets