In the present paper, we prove a sufficient condition of local regularity for suitable weak solut... more In the present paper, we prove a sufficient condition of local regularity for suitable weak solutions to the Navier-Stokes equations having axial symmetry. Our condition is an axially symmetric analog of the so-called L 3,∞ -case in the general local regularity theory. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.
A class of sufficient conditions of local regularity for suitable weak solutions to the nonstatio... more A class of sufficient conditions of local regularity for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations are discussed. The corresponding results are formulated in terms of functionals which are invariant with respect to the Navier-Stokes equations scaling. The famous Caffarelli-Kohn-Nirenberg condition is contained in that class as a particular case.
American Mathematical Society Translations: Series 2, 2010
We discuss the regularity of solutions of 2D incompressible Navier-Stokes equations forced by sin... more We discuss the regularity of solutions of 2D incompressible Navier-Stokes equations forced by singular forces. The problem is motivated by the study of complex fluids modeled by the Navier-Stokes equations coupled to a nonlinear Fokker-Planck equation describing microscopic corpora embedded in the fluid. This leads naturally to bounded added stress and hence to W −1,∞ forcing of the Navier-Stokes equations. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.
ABSTRACT We prove that weak solutions of the three-dimensional incompressible Navier-Stokes equat... more ABSTRACT We prove that weak solutions of the three-dimensional incompressible Navier-Stokes equations are smooth if the negative part of the pressure is controlled, or if the positive part of the quantity jvj 2 +2p is controlled. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.
A backward uniqueness result is proved for the heat operator with vari- able lower order terms in... more A backward uniqueness result is proved for the heat operator with vari- able lower order terms in a half-space. The main point of the result is that the boundary conditions are not controlled by the assumptions. x1. Introduction In this paper, which can be thought of as a continuation of (3) and (4), we deal with the following backward uniqueness
We consider the open problem of regularity for L3;1-solutions to the Navier-Stokes equations. We ... more We consider the open problem of regularity for L3;1-solutions to the Navier-Stokes equations. We show that the problem can be reduced to a backward uniqueness problem for the heat operator with lower order terms. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K,
In the present paper, we prove a sufficient condition of local regularity for suitable weak solut... more In the present paper, we prove a sufficient condition of local regularity for suitable weak solutions to the Navier-Stokes equations having axial symmetry. Our condition is an axially symmetric analog of the so-called L 3,∞ -case in the general local regularity theory. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.
A class of sufficient conditions of local regularity for suitable weak solutions to the nonstatio... more A class of sufficient conditions of local regularity for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations are discussed. The corresponding results are formulated in terms of functionals which are invariant with respect to the Navier-Stokes equations scaling. The famous Caffarelli-Kohn-Nirenberg condition is contained in that class as a particular case.
American Mathematical Society Translations: Series 2, 2010
We discuss the regularity of solutions of 2D incompressible Navier-Stokes equations forced by sin... more We discuss the regularity of solutions of 2D incompressible Navier-Stokes equations forced by singular forces. The problem is motivated by the study of complex fluids modeled by the Navier-Stokes equations coupled to a nonlinear Fokker-Planck equation describing microscopic corpora embedded in the fluid. This leads naturally to bounded added stress and hence to W −1,∞ forcing of the Navier-Stokes equations. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.
ABSTRACT We prove that weak solutions of the three-dimensional incompressible Navier-Stokes equat... more ABSTRACT We prove that weak solutions of the three-dimensional incompressible Navier-Stokes equations are smooth if the negative part of the pressure is controlled, or if the positive part of the quantity jvj 2 +2p is controlled. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.
A backward uniqueness result is proved for the heat operator with vari- able lower order terms in... more A backward uniqueness result is proved for the heat operator with vari- able lower order terms in a half-space. The main point of the result is that the boundary conditions are not controlled by the assumptions. x1. Introduction In this paper, which can be thought of as a continuation of (3) and (4), we deal with the following backward uniqueness
We consider the open problem of regularity for L3;1-solutions to the Navier-Stokes equations. We ... more We consider the open problem of regularity for L3;1-solutions to the Navier-Stokes equations. We show that the problem can be reduced to a backward uniqueness problem for the heat operator with lower order terms. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K,
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