id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-456	Riva, Lorenzo; Pennington, Nathan	Low regularity of non-L^2(R^n) local solutions to gMHD-alpha systems	2020	17	.pdf	application/pdf	5794	266	80	︸ ︷︷ ︸ RHS of (3.4) = γ−3 − r0 + n p0 − n p1 ≥ 0, the list reduces to γ−3 − 1 ≤ r0 ≤ γ−3 ≤ r1, r0 < n p1 , γ−1 > 1− 2r0 + r1 + 2n p0 − n p1 . 3.3. With this new bound on W1(u, v), we come back to J1 and see that J1 ≤ sup (0,T ) ∫ t 0 (t− s)−(r0−(γ−3 −1)+n/π1−n/p0)/γ−1 ‖W1(u, v)‖γ−3 −1,π1 ds ≤ C sup (0,T ) ∫ t 0 (t− s)−(r0−(γ−3 −1)+n/π1−n/p0)/γ−1 ‖u‖r0,p0‖u‖r1,p1ds = C sup (0,T ) ∫ t 0 (t− s)−(r0−(γ−3 −1)+n/π1−n/p0)/γ−1 s−a1‖u‖r0,p0sa1‖u‖r1,p1ds ≤ C‖u‖0;r0,p0‖u‖a1;r1,p1 sup (0,T ) ∫ t 0 (t− s)−(r0−(γ−3 −1)+n/π1−n/p0)/γ−1 s−a1ds < CM2T 1−(r0−(γ−3 −1)+n/π1−n/p0)/γ−1 −a1 , where the last inequality holds by Proposition 2.3, if γ−1 > r0 − (γ−3 − 1) + n π1 − n p0 + γ1a1 = r0 − (γ−3 − 1) + n ( 1 p0 + 1 p1 − r0 n )	cache/ejde-456.pdf	txt/ejde-456.txt