My research combines techniques in infinitesimal stochastic analysis and classical analysis to study (S)PDEs arising from the dynamics of fluids as well as solvent-solute mixtures of polymeric type. More specifically, I study asymptotic limits to several scaled compressible and incompressible fluid equations that are driven by deterministic and/or random forces. I also analyse well-posedness and regularity results for the Navier-Stokes equations, Euler equations, Fokker-Planck equations and various other variation of these equations.
In summary, my main research interests may be classified under the following:
- Analytical fluid dynamics,
- Analytical material science,
- Singular limit asymptotics,
- Analysis of (stochastic) partial differential equations.
Breit D, Mensah PR, 2021, An Incompressible Polymer Fluid Interacting with a Koiter Shell, Journal of Nonlinear Science, Vol:31, ISSN:0938-8974
Donatelli D, Marcati P, Mensah PR, 2021, Dissipative martingale solutions of the stochastically forced Navier-Stokes-Poisson system on domains without boundary, Nonlinear Analysis-real World Applications, Vol:57, ISSN:1468-1218
Breit D, Mensah PR, 2020, Space-time approximation of parabolic systems with variable growth, Ima Journal of Numerical Analysis, Vol:40, ISSN:0272-4979, Pages:2505-2552
Mensah PR, 2020, A Multi-scale Limit of a Randomly Forced Rotating 3-D Compressible Fluid, Journal of Mathematical Fluid Mechanics, Vol:22, ISSN:1422-6928
Donatelli D, Mensah PR, 2020, THE COMBINED INCOMPRESSIBLE QUASINEUTRAL LIMIT OF THE STOCHASTIC NAVIER-STOKES-POISSON SYSTEM, Siam Journal on Mathematical Analysis, Vol:52, ISSN:0036-1410, Pages:5090-5120