Nonhomogeneous Navier—Stokes Equations with Integrable Low—Regularity Data

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Anisotropic function spaces and maximal regularity for parabolic problems Part 1: Function spaces (2009, background): “Amann [7], [8], [9], the theory of ultra-weak solutions can also be extended to the Navier–Stokes equations.”
Stability and convergence of efficient Navier‐Stokes solvers via a commutator estimate (2007, background): “Amann recently studied very weak solutions without imposing n · g = 0 on , but only in spaces of very low regularity that exclude the present case [2].”
A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in W−1/q,q (2005, background): “In particular, Amann’s recent paper [4] for the nonstationary case was for us a motivation to study the steady case.”
A New Class of Weak Solutions of the Navier–Stokes Equations with Nonhomogeneous Data (2006, methodology): “Following Amann [3], [4] in principle we define a very weak solution as follows: Definition 1.”
Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions (2007, methodology): “In this case, following [18,1,2,7], solutions can be defined by a duality method (also called ‘the transposition method’ in [18–20]).”
Stationary Stokes, Oseen and Navier–Stokes Equations with Singular Data (2011, result): “For the non-stationary case, the existence, uniqueness and regularity of very weak solutions for the Navier-Stokes equations have been investigated (among other authors) by Amann [2,3].”