On time-local solvability of the Navier-Stokes equations in Besov spaces

By Okihiro Sawada. Advances in Differential Equations, 2001

49 citations recorded by the source corpus.

A time--local solution is constructed for the Cauchy problem of the $n$-dimensional Navier--Stokes equations when the initial velocity belongs to Besov spaces of nonpositive order. The space contains $L^\infty$ in some exponents, so our solution may not decay at space infinity. In order to use iteration scheme we have to establish the Holder type inequality for estimating bilinear term by dividing the sum of Besov norm with respect to levels of frequency. Moreover, by regularizing effect our solutions belong to $L^\infty$ for any positive time.

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

View Paper: https://www.semanticscholar.org/paper/f488c209b7fb44c4eca3e25ff908c0fbfb52f789

Citations in the corpus

• The Navier-Stokes Equations in ℝn with Linearly Growing Initial Data (2005, unknown): “, [1, 5–7, 9, 13, 14, 21, 22, 24, 28–30].”
• The Navier-Stokes equations and weak Herz spaces (2011, unknown): “There are many papers which studied Navier-Stokes equations on several function spaces, for example, [2], [17], [9], [13], [14], [21], [23], [24], [27], [30], [33], [32], [38], [40], [44], [45] etc.”