The Navier-Stokes Equations: An Elementary Functional Analytic Approach
By H. Sohr. 2012
662 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/6e51acd8483aaae2c2d64c4e4c06f843b94346cb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
Citations in the corpus
- How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? (2015, background): “incompressible NavierStokes equations possess global smooth solutions for arbitrarily large smooth initial data (e.g. under Dirichlet boundary conditions in bounded domains, cf. [23] or also [34] and [26]); also the chemotaxisonly subsystem of (1.2) obtained on letting u≡ 0 is far from understood in”
- Stabilization in a two-dimensional chemotaxis-Navier–Stokes system (2013, unknown): “…the standard estimate (1.13) reflecting energy dissipation in the Navier–Stokes system, as satisfied by any so-called turbulent solution thereof [37,28], while the second will refer to the functional F κ with appropriate κ > 0, where we have set for κ > 0 whenever n ∈ L log L((cid:6)) and c ∈ W 1…”
- Global Regularity Criterion for the 3D Navier–Stokes Equations Involving One Entry of the Velocity Gradient Tensor (2010, background): “Moreover, this strong solution is known to be unique and to depend continuously on the initial data (see, for example, [7,19, 32 ,35]).”
- Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel–Navier–Stokes system (2016, unknown): “The Stokes operator A := −P∆ with domain D(A) = W 2,2(Ω) ∩ W 1,2 0 (Ω) ∩ L 2 σ(Ω) is then sectorial in L 2 σ(Ω) and hence generates the analytic Stokes contraction semigroup (e)t≥0 and possesses densely defined fractional powers A for any α ∈ (0, 1) ([27], [12]).”
- On the uniqueness of strong solution to the incompressible Navier–Stokes equations with damping (2011, unknown): “Since then, there has been a lot of literatures devoted to investigating the issue of uniqueness and regularity (see [4,6,7,11–13,15,17–20] and references therein).”
- Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system (2015, background): “For α ∈ (0, 1), we let A denote the corresponding closed fractional power of A ([19]).”
- Well-posedness of stochastic partial differential equations with Lyapunov condition (2013, unknown): “[13,37]).”