The foundations of this outstanding book series were laid in 1944. Until the end of the
1970s, a total of 77 volumes appeared, including works of such distinguished …

A rigorous but accessible introduction to the mathematical theory of the three-dimensional
Navier–Stokes equations, this book provides self-contained proofs of some of the most …

Function Spaces Page 1 Chapter VII Function Spaces This chapter forms the core of this
volume. Besides of the classical function spaces, the basic scales of Besov and Bessel …

A carefully written Nirenberg's proof of the famous Gagliardo–Nirenberg interpolation
inequality for intermediate derivatives in Rn seems, surprisingly, to be missing in literature …

We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering
toward a weighted average heading. We consider the class of so-called $ p $-alignment …

We study the long-time hydrodynamic behavior of systems of multi-species which arise from
agent-based description of alignment dynamics. The interaction between species is …

This paper is concerned with quantitative estimates for the Navier–Stokes equations. First
we investigate the relation of quantitative bounds to the behavior of critical norms near a …

In this paper, we derive some new Gagliardo-Nirenberg type inequalities in Lorentz type
spaces without restrictions on the second index of Lorentz norms, which generalize almost …

In this paper, we derive some new Gagliardo–Nirenberg type inequalities in Lorentz type
spaces without restrictions on the second index of Lorentz norms, which generalize almost …

The main purpose of this paper is to prove some generalized Gagliardo–Nirenberg
interpolation inequalities involving the Lorentz spaces L p, α, BMO and the fractional …