Indexed by:
Abstract:
Based on a bootstrap instability method, we prove the existence of unstable strong solutions in the sense of L-1-norm to an abstract Rayleigh-Taylor (RT) problem arising from stratified viscous fluids in Lagrangian coordinates. In the proof we develop a method to modify the initial data of the linearized abstract RT problem by exploiting the existence theory of a unique solution to the stratified (steady) Stokes problem and an iterative technique, such that the obtained modified initial data satisfy the necessary compatibility conditions on boundary of the original (nonlinear) abstract RT problem. Applying an inverse transform of Lagrangian coordinates to the obtained unstable solutions and taking then proper values of the parameters, we can further obtain unstable solutions of the RT problem in viscoelastic, magnetohydrodynamics (MHD) flows with zero resistivity and pure viscous flows (with/without interface intension) in Eulerian coordinates.
Keyword:
Reprint 's Address:
Source :
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
ISSN: 0218-2025
Year: 2020
Issue: 12
Volume: 30
Page: 2299-2388
3 . 8 1 7
JCR@2020
3 . 6 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
ESI HC Threshold:50
JCR Journal Grade:1
CAS Journal Grade:1
Cited Count:
WoS CC Cited Count: 31
SCOPUS Cited Count: 28
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 3
Affiliated Colleges: