id	sid	tid	token	lemma	pos
0g354f1842q	1	1	we	we	PRON
0g354f1842q	1	2	shall	shall	AUX
0g354f1842q	1	3	consider	consider	VERB
0g354f1842q	1	4	the	the	DET
0g354f1842q	1	5	periodic	periodic	ADJ
0g354f1842q	1	6	cauchy	cauchy	ADJ
0g354f1842q	1	7	problem	problem	NOUN
0g354f1842q	1	8	for	for	ADP
0g354f1842q	1	9	a	a	DET
0g354f1842q	1	10	modified	modify	VERB
0g354f1842q	1	11	camassa	camassa	NOUN
0g354f1842q	1	12	-	-	PUNCT
0g354f1842q	1	13	holm	holm	NOUN
0g354f1842q	1	14	(	(	PUNCT
0g354f1842q	1	15	mch	mch	PROPN
0g354f1842q	1	16	)	)	PUNCT
0g354f1842q	1	17	equation	equation	NOUN
0g354f1842q	1	18	.	.	PUNCT
0g354f1842q	2	1	we	we	PRON
0g354f1842q	2	2	begin	begin	VERB
0g354f1842q	2	3	by	by	ADP
0g354f1842q	2	4	proving	prove	VERB
0g354f1842q	2	5	well	well	ADV
0g354f1842q	2	6	-	-	PUNCT
0g354f1842q	2	7	posedness	posedness	NOUN
0g354f1842q	2	8	in	in	ADP
0g354f1842q	2	9	bourgain	bourgain	NOUN
0g354f1842q	2	10	spaces	space	NOUN
0g354f1842q	2	11	for	for	ADP
0g354f1842q	2	12	sufficiently	sufficiently	ADV
0g354f1842q	2	13	small	small	ADJ
0g354f1842q	2	14	size	size	NOUN
0g354f1842q	2	15	initial	initial	ADJ
0g354f1842q	2	16	data	datum	NOUN
0g354f1842q	2	17	in	in	ADP
0g354f1842q	2	18	the	the	DET
0g354f1842q	2	19	sobolev	sobolev	NOUN
0g354f1842q	2	20	space	space	NOUN
0g354f1842q	2	21	$	$	SYM
0g354f1842q	2	22	h^s(mathbb{t})$	h^s(mathbb{t})$	NOUN
0g354f1842q	2	23	,	,	PUNCT
0g354f1842q	2	24	$	$	SYM
0g354f1842q	2	25	s=1/2	s=1/2	NOUN
0g354f1842q	2	26	$	$	NUM
0g354f1842q	2	27	,	,	PUNCT
0g354f1842q	2	28	by	by	ADP
0g354f1842q	2	29	using	use	VERB
0g354f1842q	2	30	appropriate	appropriate	ADJ
0g354f1842q	2	31	bilinear	bilinear	ADJ
0g354f1842q	2	32	estimates	estimate	NOUN
0g354f1842q	2	33	.	.	PUNCT
0g354f1842q	3	1	also	also	ADV
0g354f1842q	3	2	we	we	PRON
0g354f1842q	3	3	show	show	VERB
0g354f1842q	3	4	that	that	SCONJ
0g354f1842q	3	5	these	these	DET
0g354f1842q	3	6	bilinear	bilinear	ADJ
0g354f1842q	3	7	estimates	estimate	NOUN
0g354f1842q	3	8	do	do	AUX
0g354f1842q	3	9	not	not	PART
0g354f1842q	3	10	hold	hold	VERB
0g354f1842q	3	11	if	if	SCONJ
0g354f1842q	3	12	$	$	SYM
0g354f1842q	3	13	s<1/2$.	s<1/2$.	VERB
0g354f1842q	3	14	well	well	ADJ
0g354f1842q	3	15	-	-	PUNCT
0g354f1842q	3	16	posedness	posedness	NOUN
0g354f1842q	3	17	of	of	ADP
0g354f1842q	3	18	the	the	DET
0g354f1842q	3	19	mch	mch	NOUN
0g354f1842q	3	20	for	for	ADP
0g354f1842q	3	21	$	$	SYM
0g354f1842q	3	22	s>1/2	s>1/2	PROPN
0g354f1842q	3	23	$	$	NUM
0g354f1842q	3	24	has	have	AUX
0g354f1842q	3	25	been	be	AUX
0g354f1842q	3	26	established	establish	VERB
0g354f1842q	3	27	by	by	ADP
0g354f1842q	3	28	himonas	himonas	PROPN
0g354f1842q	3	29	and	and	CCONJ
0g354f1842q	3	30	misiol	misiol	PROPN
0g354f1842q	3	31	ek	ek	PROPN
0g354f1842q	3	32	in	in	ADP
0g354f1842q	3	33	[	[	X
0g354f1842q	3	34	hm1	hm1	NOUN
0g354f1842q	3	35	]	]	PUNCT
0g354f1842q	3	36	.	.	PUNCT
0g354f1842q	4	1	these	these	DET
0g354f1842q	4	2	results	result	NOUN
0g354f1842q	4	3	indicate	indicate	VERB
0g354f1842q	4	4	that	that	SCONJ
0g354f1842q	4	5	$	$	SYM
0g354f1842q	4	6	s=1/2	s=1/2	NOUN
0g354f1842q	4	7	$	$	NUM
0g354f1842q	4	8	may	may	AUX
0g354f1842q	4	9	be	be	AUX
0g354f1842q	4	10	the	the	DET
0g354f1842q	4	11	critical	critical	ADJ
0g354f1842q	4	12	sobolev	sobolev	NOUN
0g354f1842q	4	13	exponent	exponent	NOUN
0g354f1842q	4	14	for	for	ADP
0g354f1842q	4	15	well	well	ADV
0g354f1842q	4	16	-	-	PUNCT
0g354f1842q	4	17	posedness	posedness	NOUN
0g354f1842q	4	18	.	.	PUNCT
0g354f1842q	5	1	in	in	ADP
0g354f1842q	5	2	the	the	DET
0g354f1842q	5	3	second	second	ADJ
0g354f1842q	5	4	part	part	NOUN
0g354f1842q	5	5	of	of	ADP
0g354f1842q	5	6	this	this	DET
0g354f1842q	5	7	work	work	NOUN
0g354f1842q	5	8	we	we	PRON
0g354f1842q	5	9	show	show	VERB
0g354f1842q	5	10	that	that	SCONJ
0g354f1842q	5	11	the	the	DET
0g354f1842q	5	12	periodic	periodic	ADJ
0g354f1842q	5	13	cauchy	cauchy	ADJ
0g354f1842q	5	14	problem	problem	NOUN
0g354f1842q	5	15	for	for	ADP
0g354f1842q	5	16	the	the	DET
0g354f1842q	5	17	mch	mch	ADJ
0g354f1842q	5	18	equation	equation	NOUN
0g354f1842q	5	19	with	with	ADP
0g354f1842q	5	20	analytic	analytic	ADJ
0g354f1842q	5	21	initial	initial	ADJ
0g354f1842q	5	22	data	datum	NOUN
0g354f1842q	5	23	is	be	AUX
0g354f1842q	5	24	analytic	analytic	ADJ
0g354f1842q	5	25	in	in	ADP
0g354f1842q	5	26	the	the	DET
0g354f1842q	5	27	space	space	NOUN
0g354f1842q	5	28	variable	variable	NOUN
0g354f1842q	5	29	$	$	SYM
0g354f1842q	5	30	x$	x$	X
0g354f1842q	5	31	for	for	ADP
0g354f1842q	5	32	time	time	NOUN
0g354f1842q	5	33	near	near	ADP
0g354f1842q	5	34	zero	zero	NUM
0g354f1842q	5	35	.	.	PUNCT
0g354f1842q	6	1	by	by	ADP
0g354f1842q	6	2	differentiating	differentiate	VERB
0g354f1842q	6	3	the	the	DET
0g354f1842q	6	4	equation	equation	NOUN
0g354f1842q	6	5	and	and	CCONJ
0g354f1842q	6	6	the	the	DET
0g354f1842q	6	7	initial	initial	ADJ
0g354f1842q	6	8	condition	condition	NOUN
0g354f1842q	6	9	with	with	ADP
0g354f1842q	6	10	respect	respect	NOUN
0g354f1842q	6	11	to	to	ADP
0g354f1842q	6	12	$	$	SYM
0g354f1842q	6	13	x$	x$	X
0g354f1842q	6	14	we	we	PRON
0g354f1842q	6	15	obtain	obtain	VERB
0g354f1842q	6	16	a	a	DET
0g354f1842q	6	17	sequence	sequence	NOUN
0g354f1842q	6	18	of	of	ADP
0g354f1842q	6	19	initial	initial	ADJ
0g354f1842q	6	20	value	value	NOUN
0g354f1842q	6	21	problems	problem	NOUN
0g354f1842q	6	22	of	of	ADP
0g354f1842q	6	23	kdv	kdv	ADJ
0g354f1842q	6	24	-	-	PUNCT
0g354f1842q	6	25	type	type	NOUN
0g354f1842q	6	26	equations	equation	NOUN
0g354f1842q	6	27	.	.	PUNCT
0g354f1842q	7	1	these	these	PRON
0g354f1842q	7	2	,	,	PUNCT
0g354f1842q	7	3	written	write	VERB
0g354f1842q	7	4	in	in	ADP
0g354f1842q	7	5	the	the	DET
0g354f1842q	7	6	form	form	NOUN
0g354f1842q	7	7	of	of	ADP
0g354f1842q	7	8	integral	integral	ADJ
0g354f1842q	7	9	equations	equation	NOUN
0g354f1842q	7	10	,	,	PUNCT
0g354f1842q	7	11	define	define	VERB
0g354f1842q	7	12	a	a	DET
0g354f1842q	7	13	mapping	mapping	NOUN
0g354f1842q	7	14	on	on	ADP
0g354f1842q	7	15	a	a	DET
0g354f1842q	7	16	banach	banach	NOUN
0g354f1842q	7	17	space	space	NOUN
0g354f1842q	7	18	whose	whose	DET
0g354f1842q	7	19	elements	element	NOUN
0g354f1842q	7	20	are	be	AUX
0g354f1842q	7	21	sequences	sequence	NOUN
0g354f1842q	7	22	of	of	ADP
0g354f1842q	7	23	functions	function	NOUN
0g354f1842q	7	24	equipped	equip	VERB
0g354f1842q	7	25	with	with	ADP
0g354f1842q	7	26	a	a	DET
0g354f1842q	7	27	norm	norm	NOUN
0g354f1842q	7	28	expressing	express	VERB
0g354f1842q	7	29	the	the	DET
0g354f1842q	7	30	cauchy	cauchy	ADJ
0g354f1842q	7	31	estimates	estimate	NOUN
0g354f1842q	7	32	in	in	ADP
0g354f1842q	7	33	terms	term	NOUN
0g354f1842q	7	34	of	of	ADP
0g354f1842q	7	35	the	the	DET
0g354f1842q	7	36	kdv	kdv	ADJ
0g354f1842q	7	37	norms	norm	NOUN
0g354f1842q	7	38	of	of	ADP
0g354f1842q	7	39	the	the	DET
0g354f1842q	7	40	components	component	NOUN
0g354f1842q	7	41	introduced	introduce	VERB
0g354f1842q	7	42	in	in	ADP
0g354f1842q	7	43	the	the	DET
0g354f1842q	7	44	works	work	NOUN
0g354f1842q	7	45	of	of	ADP
0g354f1842q	7	46	bourgain	bourgain	PROPN
0g354f1842q	7	47	,	,	PUNCT
0g354f1842q	7	48	kenig	kenig	NOUN
0g354f1842q	7	49	,	,	PUNCT
0g354f1842q	7	50	ponce	ponce	ADV
0g354f1842q	7	51	,	,	PUNCT
0g354f1842q	7	52	vega	vega	ADJ
0g354f1842q	7	53	and	and	CCONJ
0g354f1842q	7	54	others	other	NOUN
0g354f1842q	7	55	.	.	PUNCT
0g354f1842q	8	1	by	by	ADP
0g354f1842q	8	2	proving	prove	VERB
0g354f1842q	8	3	appropriate	appropriate	ADJ
0g354f1842q	8	4	bilinear	bilinear	ADJ
0g354f1842q	8	5	estimates	estimate	NOUN
0g354f1842q	8	6	we	we	PRON
0g354f1842q	8	7	show	show	VERB
0g354f1842q	8	8	that	that	SCONJ
0g354f1842q	8	9	this	this	DET
0g354f1842q	8	10	mapping	mapping	NOUN
0g354f1842q	8	11	is	be	AUX
0g354f1842q	8	12	a	a	DET
0g354f1842q	8	13	contraction	contraction	NOUN
0g354f1842q	8	14	,	,	PUNCT
0g354f1842q	8	15	and	and	CCONJ
0g354f1842q	8	16	therefore	therefore	ADV
0g354f1842q	8	17	we	we	PRON
0g354f1842q	8	18	obtain	obtain	VERB
0g354f1842q	8	19	a	a	DET
0g354f1842q	8	20	solution	solution	NOUN
0g354f1842q	8	21	whose	whose	DET
0g354f1842q	8	22	derivatives	derivative	NOUN
0g354f1842q	8	23	in	in	ADP
0g354f1842q	8	24	the	the	DET
0g354f1842q	8	25	space	space	NOUN
0g354f1842q	8	26	variable	variable	NOUN
0g354f1842q	8	27	satisfy	satisfy	VERB
0g354f1842q	8	28	the	the	DET
0g354f1842q	8	29	cauchy	cauchy	ADJ
0g354f1842q	8	30	estimates	estimate	NOUN
0g354f1842q	8	31	.	.	PUNCT