Danchin, R. Global existence in critical spaces for compressible Navier-Stokes equations. (English) Zbl 0958.35100 Invent. Math. 141, No. 3, 579-614 (2000). The author investigates global solutions for isentropic compressible fluids in \(\mathbb{R}^n, n\geq 2\) using critical spaces, i.e. spaces in which the associated norm is invariant under the transformation \((\rho, u)\mapsto (\rho(l\cdot), lu(l\cdot))\) (up to a constant independent of \(l\)). In the settings of homogeneous Besov spaces with minimal regularity \(n/2\) for the velocity \(u\) and \(n/2-1\) for the density \(\rho\), with initial data \((u_0,\rho_0)\) close to a stable equilibrium \((0, \bar\rho)\), and under the additional assumption \(\rho_0-\bar\rho\in B^{n/2-1}\) he shows existence, regularity, and uniqueness (the latter for \(n\geq 3\), for \(n=2\) one needs higher regularity). Reviewer: Uwe Kähler (Aveiro) Cited in 5 ReviewsCited in 180 Documents MSC: 35Q30 Navier-Stokes equations 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35Q35 PDEs in connection with fluid mechanics Keywords:global strong solutions; isentropic compressible fluids; Besov spaces PDF BibTeX XML Cite \textit{R. Danchin}, Invent. Math. 141, No. 3, 579--614 (2000; Zbl 0958.35100) Full Text: DOI