You are not logged in |
A maximal regularity approach to compressible mixtures"
- Speaker(s)
- Tomasz Piasecki
- Affiliation
- IMSiM
- Date
- Oct. 29, 2020, 12:30 p.m.
- Information about the event
- Zoom meeting
- Seminar
- Seminar of Mathematical Physics Equations Group
Join Zoom Meeting
https://us02web.zoom.us/j/81583752461?pwd=c2xXN0hoQVBVc2JLNmNYRHkxTzV4UT09
Meeting ID: 815 8375 2461
Passcode: 495149
--------------------------------------------------------------------------------------------------------------
I will present recent results obtained in collaboration with Yoshihiro
Shibata and Ewelina Zatorska. We investigate the well posedness of a
system describing flow of a mixture of compressible constituents.
The system in composed of Navier-Stokes equations coupled with equations
describing balance of fractional masses. A crucial property is that the
system is non-symmetric and only degenerate parabolic.
However, it reveals a structure which allows to transform it to a
symmetric parabolic problem using appropriate change of unknowns. In order
to treat the transformed problem we write it in Lagrangian coordinates and
linearize.
For the related linear problem we show a Lp-Lq maximal regularity estimate
applying the theory of R-bounded solution operators. This estimate allows
to show local existence and uniqueness. Next, assuming additionally
boundedness of the domain we extend the maximal regularity estimate and
show exponential decay property for the linear problem. This allow us to
show global well-posedness of the original problem for small data.
Shibata and Ewelina Zatorska. We investigate the well posedness of a
system describing flow of a mixture of compressible constituents.
The system in composed of Navier-Stokes equations coupled with equations
describing balance of fractional masses. A crucial property is that the
system is non-symmetric and only degenerate parabolic.
However, it reveals a structure which allows to transform it to a
symmetric parabolic problem using appropriate change of unknowns. In order
to treat the transformed problem we write it in Lagrangian coordinates and
linearize.
For the related linear problem we show a Lp-Lq maximal regularity estimate
applying the theory of R-bounded solution operators. This estimate allows
to show local existence and uniqueness. Next, assuming additionally
boundedness of the domain we extend the maximal regularity estimate and
show exponential decay property for the linear problem. This allow us to
show global well-posedness of the original problem for small data.
