- Title Information
- Title
- Stability of certain geophysical structures in fluid dynamics via dispersive analysis
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Ko, Haram
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Pausader, Benoit
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Gomez-Serrano, Javier
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Guo, Yan
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2026
- Physical Description
- Extent
- 187, 177 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2026
- Genre (aat)
- theses
- Abstract
- This thesis establishes the stability of rotation in the 3D compressible Euler equation
and incompressible Navier-Stokes equation, and the stability of linear stratification in
the 2D Boussinesq equation. Using the common factor that these steady states induce
dispersion, I establish a systematic method for linear analysis. This is explained through
two different systems to highlight that the method is versatile enough to work for different
dispersion relations in different systems. Combined with the energy estimates, this
produces long-time stabilities of the respective steady states. Finally, I prove the global
stability for one of these systems using a mix of paradifferential calculus, the spacetime
resonance method, and the aforementioned linear theory.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00893484")
- Topic
- Differential equations, Partial
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20260516