Smooth or singular solutions to the Navier-Stokes system ?

By Marco Cannone, Grzegorz Karol Karch. 2002

152 citations recorded by the source corpus.

Abstract The existence of singular solutions of the incompressible Navier–Stokes system with singular external forces, the existence of regular solutions for more regular forces as well as the asymptotic stability of small solutions (including stationary ones), and a pointwise loss of smoothness for solutions are proved in the same function space of pseudomeasure type.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3855ae36aa4299192afdc1e74fe74985b12d5687

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Global well-posedness for the micropolar fluid system in critical Besov spaces (2010, unknown): “Recently, inspired by the work of Cannone and Karch [5] on the compressible Navier-Stokes equations, V.-Roa and Ferreira [14] proved the wellposedness of the generalized micropolar fluids system in the pseudo-measure space which is denoted by PMa-space whose Fourier transform verifies sup R3 |ξ|a|f̂”
Chapter 3 - Harmonic Analysis Tools for Solving the Incompressible Navier–Stokes Equations (2005, background): “As such, if c is small enough, the existence of these solutions can be ensured as well via the fixed point algorithm as in [42,40].”
On Landau’s solutions of the Navier–Stokes equations (2006, background): “209] and was also calculated in [6].”
About the Regularized Navier–Stokes Equations (2003, background): “✷ Remark 4.1 Homogeneity properties of equation (2.1) imply that if u solves the Cauchy problem, then the rescaled function uλ(x, t) = λu(λx, λ 2t) is also a solution for each λ > 0.”