{"paper":{"title":"Analysis of 2+1 diffusive-dispersive PDE arising in river braiding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Charis Tsikkou, Saleh Tanveer","submitted_at":"2014-05-12T19:34:37Z","abstract_excerpt":"We present local existence and uniqueness results for the following $2+1$ dispersive diffusive equation due to P. Hall arising in modeling of river braiding: $$u_{yyt} - \\gamma u_{xxx} -\\alpha u_{yyyy} - \\beta u_{yy} + \\left (u^2 \\right)_{xyy} = 0$$ for $(x,y) \\in [0, 2\\pi] \\times [0, \\pi]$, $t> 0$, with boundary condition $u_{y}=0=u_{yyy}$ at $y=0$ and $y=\\pi$ and $2\\pi$ periodicity in $x$, using a contraction mapping argument in a Bourgain-type space $T_{s,b}$. We also show that the energy $\\| u \\|^2_{L^2} $ and cumulative dissipation $\\int_0^t \\| u_y \\|_{L^2}^2 dt$ are globally controlled i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2890","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"}