The Navier-Stokes equations: existence theorems and energy equalities

DOI10.1134/S1064562411030446zbMath1234.35187OpenAlexW2063159167MaRDI QIDQ656355

S. E. Pastukhova, Vasilii V. Jikov

Publication date: 17 January 2012

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562411030446

zbMATH Keywords

weak solutionsGalerkin approximationsintegral identityenergy inequalitygeneralized Navier-Stokes equationsregularized problems

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Weak solutions to PDEs (35D30)

Cites Work

• New approach to the solvability of generalized Navier-Stokes equations
• Compensated compactness principle and solvability of generalized Navier-Stokes equations
• On the compensated compactness principle
• Nonlinear elliptic and parabolic equations involving measure data
• On partial regularity results for the navier-stokes equations
• A new proof of the Caffarelli-Kohn-Nirenberg theorem
• Partial regularity of suitable weak solutions of the navier-stokes equations
• On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications