Open AccessRegularity of solutions to non-stationary Navier–Stokes equations
Author(s) -
Е. В. Амосова
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1268/1/012007
Subject(s) - solenoidal vector field , uniqueness , mathematics , regularization (linguistics) , vector field , navier–stokes equations , mathematical analysis , compressibility , domain (mathematical analysis) , weak solution , function (biology) , physics , computer science , geometry , mechanics , artificial intelligence , evolutionary biology , biology
This paper covers a non-stationary system of Navier–Stokes equations for incompressible fluids. A regularized problem is considered that factors in the velocity field being relaxed to a solenoidal field; this problem is used to prove the pressure function exists almost everywhere in the domain for the Hopf class solutions. The proposed regularization proves there exist more regular weak solutions to the initial problem that do not impose smallness restrictions on the input data. The theorem of uniqueness is proven for the 2D case.