{
  "annotation_id": "55caab88-b636-46dd-8416-9db22501116d",
  "date_created": "2026-02-17T05:53:20.217000Z",
  "date_modified": "2026-02-17T05:53:20.217000Z",
  "file_hash": "9be36ba1936bbfe2e3f77a7e1c5af466372318bd0fa3b70a52a8012fa69f5e9f",
  "private": false,
  "record": {
    "abstract": "We consider parabolic variational inequalities in a Hilbert space $V$, which have a non-monotone nonlinearity of Navier--Stokes type represented by a bilinear operator $B: V \\times V \\to V\u0027$ and a monotone type nonlinearity described by a convex, proper, and lower-semicontinuous functional $\\varphi : V \\to (-\\infty, +\\infty]$. Existence and uniqueness of a local-in-time strong solution in a maximal-$L^2$-regularity class and in a Kiselev--Ladyzhenskaya class are proved by discretization in time (also known as Rothe\u0027s method), provided that a corresponding stationary Stokes problem admits a regularity structure better than $V$ (which is typically $H^2$-regularity in case of the Navier--Stokes equations). Since we do not assume the cancelation property $\\left\u003c B(u, v), v \\right\u003e = 0$, in applications we may allow for broader boundary conditions than those treated by the existing literature.",
    "arxiv_id": "2601.09190",
    "authors": [
      "Takahito Kashiwabara"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Local-in-time strong solvability of Navier--Stokes type variational inequalities by Rothe\u0027s method",
    "url": "https://arxiv.org/abs/2601.09190",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "302ccdf2-33d7-4715-9efc-b016c22b6780",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}