Diagonalization of indefinite saddle point forms
Luka Grubi\v{s}i\'c, Vadim Kostrykin, Konstantin A. Makarov, Stephan, Schmitz, Kre\v{s}imir Veseli\'c
TL;DR
This paper establishes conditions for block diagonalization of indefinite saddle point forms and associated operators, extending to semi-bounded cases with applications to fluid dynamics.
Contribution
It provides new sufficient conditions for block diagonalization of indefinite forms and operators, including semi-bounded cases, with practical examples from fluid dynamics.
Findings
Conditions for block diagonalization of indefinite forms
Refined results for semi-bounded cases
Application to the block Stokes Operator in fluid dynamics
Abstract
We obtain sufficient conditions that ensure block diagonalization (by a direct rotation) of sign-indefinite symmetric sesquilinear forms as well as the associated operators that are semi-bounded neither from below nor from above. In the semi-bounded case, we refine the obtained results and, as an example, revisit the block Stokes Operator from fluid dynamics.
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