Navier-Stokes Equations with Lower Bounds on the Pressure

By G A Seregin, Vladimír Sverák. 2002

140 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3ada85bcfba6f1f2f1a4bc8ba02bde0d8ee00a4a

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In Applied Mathematics

In Computational Mechanics

In Mathematical Physics

Citations in the corpus

Regularity Criteria for the Three-dimensional Navier-Stokes Equations (2008, background): “Moreover, that have also been some articles dedicated to the study the global regularity of the 3D Navier–Stokes equation by providing some sufficient conditions on the pressure (cf. e.g., [3], [10], [22], [38], [48]).”
Log Improvement of the Prodi-Serrin Criteria for Navier-Stokes Equations (2007, background): “Let us also cite a condition involving the lower bound of the pressure introduced by Seregin and Sverak in [19], and conditions involving only one of the component of u (see Penel and Pokorny [17], He [9], and Zhou [23, 26]).”
L3,∞-solutions of the Navier-Stokes equations and backward uniqueness (2003, background): “As shown in [39], there is a sequence of positive numbers Rk such that Rk → 0 as k → +∞ and A(Rk) ≡ sup t0−R(2)k t t0 1 Rk ∫”
Nonuniqueness of weak solutions to the Navier-Stokes equation (2017, unknown): “Based on the natural scaling of the equations v(x, t) 7→ vλ(x, t) = λv(λx, λ2t), a number of partial regularity results have been established [46, 7, 41, 37, 54, 35]; the local existence for the Cauchy problem has been proven in scaling-invariant spaces [30, 32, 28]; and conditional regularity has b”
A new proof of partial regularity of solutions to Navier-Stokes equations (2007, background): “Seregin and Sverak showed the full regularity of suitable solutions under a natural (but still unproved) condition on the pressure in [20].”
Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations (2006, background): “Special cases (1/p,1/q) = (1/3,1/3) and (1/2,0) were obtained in [39] and [ 30 ], respectively.”
Global Regularity Criterion for the 3D Navier–Stokes Equations Involving One Entry of the Velocity Gradient Tensor (2010, unknown): “, [3], [4], [5], [8], [17], [30], [39]).”
A Strong Regularity Result for Parabolic Equations (2004, background): “It seems that all previous regularity results either make some global restrictions on P or on the initial value u0. We mention the recent interesting result of Seregin and Sverak [ SS ].”