Stochastic Partial Differential Equations in Fluid Convection: Mathematical Developments and Physical Applications

4 luglio 2017
4 luglio 2017
Contatti: 
Staff Dipartimento di Matematica

Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3898-1980.
dept.math [at] unitn.it

Seminario congiunto Dipartimento di Matematica – Centro Internazionale per la Ricerca Matematica (CIRM)

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari “-1”
Ore 11:00

  • Relatori: Juraj Földes, Nathan Glatt-Holtz, Geordie Richards (Partecipanti al programma Research in Pairs del CIRM)

Abstract:
Convection, heat transfer due to fluid flow driven by buoyancy forces arising from differences in density, is a fundamental physical mechanism important in such a wide variety of settings as climate, plate tectonics and stelar physics.  Such fluid flows are typically driven by heating mechanisms acting both at boundaries in the bulk which have components of an essentially stochastic character. Thus, the study of stochastic partial differential equations (SPDEs) in this context is natural physically.   Here a paradigmatic model is the stochastic Bouusinesq equations— essentially the incompressible Navier-Stokes system coupled to equations for the density of the fluid (temperature, salinity or some other scalar quantity) where stochastic terms appear.  Since many situations of interest reach well beyond realistic laboratory settings or direct observation, the analytical understanding of these equations are of essential scientific interest.   On the other hand, it turns out that this setting of stochastic convection leads to new mathematical challenges at the intersection of PDEs functional analysis and probability which are significant beyond
immediate physical applications.    

Our research group has focused on the stochastic Bouusinesq equations and related stochastic fluids equations.   We have addressed questions in the ergodic theory of hypoelliptic infinite dimensional stochastic systems and considered singular parameter limit problems using insights from optimal transport theory.  Currently we are developing methods to address the onset of instability from basic`conductive states' in these systems. 

 

Referente: Marco Andreatta