{"paper":{"title":"On Abstract $\\mathrm{grad}-\\mathrm{div}$ Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Marcus Waurick, Rainer Picard, Sascha Trostorff, Stefan Seidler","submitted_at":"2015-04-08T14:52:01Z","abstract_excerpt":"For a large class of dynamical problems from mathematical physics the skew-selfadjointness of a spatial operator of the form $A=\\left(\\begin{array}{cc} 0 & -C^{*}\\\\ C & 0 \\end{array}\\right)$, where $C:D\\left(C\\right)\\subseteq H_{0}\\to H_{1}$ is a closed densely defined linear operator, is a typical property. Guided by the standard example, where $C=\\mathrm{grad}=\\left(\\begin{array}{c} \\partial_{1}\\\\ \\vdots\\\\ \\partial_{n} \\end{array}\\right)$ (and $-C^{*}=\\mathrm{div}$, subject to suitable boundary constraints), an abstract class of operators $C=\\left(\\begin{array}{c} C_{1}\\\\ \\vdots\\\\ C_{n} \\end"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02456","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}