{"paper":{"title":"Global and blow-up radial solutions for quasilinear elliptic systems arising in the study of viscous, heat conducting fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gurpreet Singh, Jacques Giacomoni, Marius Ghergu","submitted_at":"2018-08-01T16:30:28Z","abstract_excerpt":"We study positive radial solutions of quasilinear elliptic systems with a gradient term in the form $$ \\left\\{ \\begin{aligned} \\Delta_{p} u&=v^{m}|\\nabla u|^{\\alpha}&&\\quad\\mbox{ in }\\Omega,\\\\ \\Delta_{p} v&=v^{\\beta}|\\nabla u|^{q} &&\\quad\\mbox{ in }\\Omega, \\end{aligned} \\right. $$ where $\\Omega\\subset\\R^N$ $(N\\geq 2)$ is either a ball or the whole space, $1<p<\\infty$, $m, q>0$, $\\alpha\\geq 0$, $0\\leq \\beta\\leq m$ and $(p-1-\\alpha)(p-1-\\beta)-qm\\neq 0$. We first classify all the positive radial solutions in case $\\Omega$ is a ball, according to their behavior at the boundary. Then we obtain tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00407","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"}