@article{Sango_2023, title={Stochastic Navier–Stokes variational inequalities with unilateral boundary conditions: probabilistic weak solvability}, volume={75}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6665}, DOI={10.37863/umzh.v75i4.6665}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>UDC 519.21</p> </div> </div> </div> <p>We initiate the investigation of stochastic Navier–Stokes variational inequalities involving unilateral boundary conditions and nonlinear forcings driven by Wiener processes for which we establish the existence of a probabilistic weak (or martingale) solution.<span class="Apple-converted-space"> </span>Our approach involves an intermediate penalized problem whose weak solution is obtained by means of Galerkin’s method in combination with some analytic and probabilistic compactness results.<span class="Apple-converted-space"> </span>The required probabilistic weak solution of the stochastic Navier–Stokes variational inequality is consecutively obtained through the limit transition in the penalized problem.<span class="Apple-converted-space"> </span>The main result is new for stochastic Navier–Stokes variational inequalities. It is a stochastic counterpart of the work of Brezis on deterministic Navier–Stokes variational inequalities and generalizes several previous results on stochastic Navier-Stokes equations to stochastic Navier–Stokes variational inequalities with unilateral boundary conditions.</p>}, number={4}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Sango, M.}, year={2023}, month={May}, pages={523 - 541} }