Lp-approach to steady flows of viscous compressible fluids in exterior domains

On the two-dimensional steady-state problem of a viscous gas in an exterior domain

“…To show existence of solutions for the linear system (2.4), we use the following decomposition method introduced by Novotný and Padula [45]:…”

“…Problem (2.4 ) with v ∞ = 0 in exterior threedimensional domains was investigated by Novotný and Padula [45] (see also Novotný [43], [44], Padula [49], [50], Novotný and Penel [48]). 3 However, to our knowledge, no results are available in twodimensional case.…”

“…The form of these estimates is conjectured by the well known structure of 2-D Oseen tensor (especially by its summability and rescaling properties), and from what is known for 2-D exterior Oseen problem. In this respect, the splitting inspired by [45] (called the decomposition method), plays an essential role.…”

“…II, Chapters. 9, 10), [27], [31], [32], [35], [40], [41], [47], [56]) and, more recently, also for the compressible case (see [37], [38], [39], [36], [44], [45], [48]). In general, exterior fluid dynamical problems present further essential difficulties compared to the interior ones (bounded domains).…”

On The Steady Transport Equation

“…One of its recent applications has been to the so called steady transport equation, which plays a fundamental role related to mass conservation in the existence theory for steady compressible viscous flow; see Padula [20]' [21J, [22], [23], [24], Beirao da Veiga [1], Valli [26], Farwig [6], Novotny and Padula [18], and Novotny [15], [16]. However, in the case of the steady transport equation, the tools which were developed for the general theory of degenerate second order equations seem overly abstract and difficult.…”