The Role of the Pressure in the Partial Regularity Theory for Weak Solutions of the Navier–Stokes Equations

@article{Chamorro2016TheRO,
  title={The Role of the Pressure in the Partial Regularity Theory for Weak Solutions of the Navier–Stokes Equations},
  author={D. Chamorro and P. Lemari{\'e}–Rieusset and Kawther Mayoufi},
  journal={Archive for Rational Mechanics and Analysis},
  year={2016},
  volume={228},
  pages={237-277}
}
We study the role of the pressure in the partial regularity theory for weak solutions of the Navier–Stokes equations. By introducing the notion of dissipative solutions, due to Duchon and Robert (Nonlinearity 13:249–255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin’s local regularity criterion. 
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References

SHOWING 1-10 OF 24 REFERENCES
On interior regularity criteria for weak solutions of the navier-stokes equations
  • 106
  • Highly Influential
  • PDF
Morrey space techniques applied to the interior regularity problem of the Navier-Stokes equations
  • 16
Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations
  • 249
  • Highly Influential
On partial regularity for the Navier-Stokes equations
  • 37
  • Highly Influential
  • PDF
A new proof of partial regularity of solutions to Navier-Stokes equations
  • 108
  • Highly Influential
  • PDF
On Partial Regularity of Suitable Weak Solutions to the Three-Dimensional Navier—Stokes equations
  • 237
  • Highly Influential
On partial regularity results for the navier‐stokes equations
  • 293
  • Highly Influential
A new proof of the Caffarelli‐Kohn‐Nirenberg theorem
  • 402
Conditions for the Local Boundedness of Solutions of the Navier–Stokes System in Three Dimensions
  • 22
  • Highly Influential
  • PDF
The Navier-Stokes Problem in the 21st Century
  • 140
  • Highly Influential
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