• Corpus ID: 238857028

Local regularity near boundary for the Stokes and Navier-Stokes equations

@inproceedings{Chang2021LocalRN,
  title={Local regularity near boundary for the Stokes and Navier-Stokes equations},
  author={Tongkeun Chang and Kyungkeun Kang},
  year={2021}
}
We are concerned with local regularity of the solutions for the Stokes and Navier-Stokes equations near boundary. Firstly, we construct a bounded solution but its normal derivatives are singular in any L with 1 < p locally near boundary. On the other hand, we present criteria of solutions of the Stokes equations near boundary to imply that the gradients of solutions are bounded (in fact, even further Hölder continuous). Finally, we provide examples of solutions whose local regularity near… 

References

SHOWING 1-10 OF 28 REFERENCES
On the local regularity of suitable weak solutions to the generalized Navier–Stokes equations
We consider the Navier–Stokes equations in three spatial dimensions and present a new proof of the Caffarelli–Kohn–Nirenberg theorem, based on a generalized notion of a local suitable weak solution,
Finite energy Navier-Stokes flows with unbounded gradients induced by localized flux in the half-space
For the Stokes system in the half space, Kang [Math. Ann. 2005] showed that a solution generated by a compactly supported, Hölder continuous boundary flux may have unbounded normal derivatives near
Estimates of anisotropic Sobolev spaces with mixed norms for the Stokes system in a half-space
We are concerned with the non-stationary Stokes system with non-homogeneous external force and non-zero initial data in $${\mathbb {R}}^n_+ \times (0,T)$$R+n×(0,T). We obtain new estimates of
On estimates of solutions of the non-stationary Stokes problem in anisotropic Sobolev spaces and on estimates for the resolvent of the Stokes operator
In this paper, which is mainly of a survey nature, a coercive estimate is proved in Sobolev spaces with a mixed norm to solve the non-stationary Stokes problem (with non-zero divergence) in bounded
On Caccioppoli's inequalities of Stokes equations and Navier-Stokes equations near boundary
We study Caccioppoli's inequalities of the non-stationary Stokes equations and Navier-Stokes equations. Our analysis is local near boundary and we prove that, in contrast to the interior case, the
Unbounded normal derivative for the Stokes system near boundary
Abstract.We study local boundary regularity for the Stokes system. We show that, unlike in the interior case, non-local effects can lead to a violation of local regularity in the spatial variables
The Initial Boundary-Value Problem for a Generalized Stokes System in a Half-Space
AbstractThe paper contains the construction of a solution of the Cauchy–Dirichlet problem in the half-space $$\mathbb{R}_ + ^3 $$ for a family of systems of differential equations that includes a
On Maximum Modulus Estimates of the Navier-Stokes Equations with Nonzero Boundary Data
We consider discontinuous influx for the Navier--Stokes flow and construct a solution that is unbounded in a neighborhood of a discontinuous point of given bounded boundary data for any dimension l...
Some Estimates near the Boundary for Solutions to the Nonstationary Linearized Navier–Stokes Equations
In the present paper, new local estimates near the boundary are established for solutions to the nonstationary linearized Navier–Stokes equations are established. Bibliography: 8 titles.
Caccioppoli type inequality for non-Newtonian Stokes system and a local energy inequality of non-Newtonian Navier-Stokes equations without pressure
We prove a Caccioppoli type inequality for the solution of a parabolic system related to the nonlinear Stokes problem. Using the method of Caccioppoli type inequality, we also establish the existence
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