Uniformly Local L p Estimate for 2-D Vorticity Equation and Its Application to Euler Equations with Initial Vorticity in bmo

Remark on Single Exponential Bound of the Vorticity Gradient for the Two-Dimensional Euler Flow Around a Corner

“…To state our result precisely, we rewrite (1.1) into the whole plane R 2 , by change of valuables and reflection argument. By [9,10] (see also [8]), we see that the solution uniquely exists in [13]). The following is the main theorem.…”

Remarks on Global Solvability of 2-D Boussinesq Equations with Non-Decaying Initial Data

“…We show that the time-local solution given in Lemma 3.1 can be extended to a global solution. Based on (3.1) and (3.2), we assume that u 0 A W 2; y , y 0 A _ B B Now, we shall show (5.4) using Lemma 3.2, (I.E.B) 1 and a method similar to that described in [28]. (See also Serfati [27], Vishik [31] and [26].)…”

A Remark on L ∞ Solutions to the 2-D Navier–Stokes Equations

“…It is clear that v is a weak solution of the Euler equations satisfying (1.2). The details are found in [15].…”