A
Applications, ,
13,
15,
41,
65,
72,
76,
109,
132,
145,
170,
175,
183
B
Banach function space, ,
56,
102
Bogovskiĭ operator,
28,
35,
49,
69,
71,
72,
92,
95,
111,
117,
132,
140–142
Boundedness,
38,
85,
128,
132,
133,
148,
156,
157,
191,
219
C
Conditions,
23,
27,
29,
32–34,
36,
40,
49,
54,
59,
60,
64,
69,
70,
187,
188
Constant,
10,
13,
15,
22,
33,
36–42,
44,
48,
49,
53–55,
57–59,
61–66,
69,
70,
105–107,
125,
126,
134
Continuity,
15,
35,
80,
92,
96,
102,
124,
132–134,
142,
182,
191,
211
Continuous function, , , ,
13,
27,
61,
64,
66,
67,
92,
112,
146,
184,
204
Continuous local martingale,
167
Convective term,
23,
24,
27,
54,
90,
109,
146,
147,
149,
152
Convergences,
75,
95,
97,
110–112,
132,
184,
189,
202,
205,
206,
211,
215–217
D
Definition of Luxemburg norm,
39,
51,
52
Divergence equation,
26,
35
Doob–Meyer decomposition,
163,
164
E
Equivalence classes, ,
165
Estimates,
12,
15–17,
19,
21,
72,
74–76,
82,
83,
87,
88,
106,
107,
123–125,
129,
130,
134,
135,
143,
157,
201
Existence, ,
13,
14,
22,
23,
27,
31,
44,
54,
72,
94,
97,
108,
109,
146–149,
154,
155,
185,
186,
188
F
Framework, functional analytic, ,
101
Fubini's theorem,
17,
123
Function spaces, , , ,
71finite dimensional,
72,
80
Functions,
3–5,
7–14,
20–23,
26–32,
34–36,
47,
48,
54,
59,
63–66,
72–74,
89–92,
101–104,
111–113,
115–118,
121
G
Gradients,
11,
12,
19,
21,
30,
31,
45,
71,
75,
81,
106,
115,
125,
186,
191
H
I
J
Jakubowski–Skorokhod theorem,
212,
214
K
Kondrachov's theorem,
24,
27
Korn's inequality,
24,
29,
30,
32,
35,
78,
79,
93,
155,
197
L
Lipschitz truncation,
11–18,
27,
28,
71,
75–77,
83,
89,
92,
104,
105,
112,
113,
115,
188
M
Monotone operator theory,
23–25,
109,
110,
146,
151,
189,
206,
209,
217,
218
N
Norm, , ,
10,
25,
31–33,
36,
47,
55,
56,
62,
81–83,
102–104,
111,
124,
126
O
Operator,
29,
40,
45,
47,
49,
50,
63,
72,
93,
128,
191,
193,
202linear projection,
60,
61
Orlicz–Sobolev space,
10,
32
P
Pressure,
22,
23,
30,
31,
54,
89,
91–93,
97,
108,
111,
145,
146,
155,
157,
185,
188,
189,
192,
210
Probability space,
161,
162,
168–171,
174–176,
178,
183,
184,
202–205,
207,
210,
212,
214,
215
Properties, ,
20,
37–39,
49,
50,
63,
71,
72,
74,
76,
77,
83,
105,
106,
115–117,
122–124,
127–129,
138,
139,
161,
162
Q
R
Representation formula, ,
61,
63,
66
S
Sequence, , ,
11,
16,
24,
27,
52,
61,
66,
67,
77,
91,
92,
101,
103,
128,
166,
167,
177
Sequence of approximated solutions,
25,
109
Solenoidal Lipschitz truncation,
71–74,
89,
92,
95,
115,
132,
135,
145,
146,
154
Solenoidal test functions,
92,
117
Space, , ,
11,
36,
47,
54,
60,
63,
77,
91,
102,
117,
146,
147,
165,
166,
194
Space of test functions,
94,
147
Stationary flows, ,
22,
89
Stationary problems,
71,
110
Stochastic Fubini theorem,
176
Stochastic heat equation,
173,
177
Stochastic integration,
161
Stochastic power law fluids,
186
Subsequence,
24,
26,
52,
61,
77,
83,
84,
91,
94,
95,
110,
128,
131,
149,
152,
155,
156,
209–211
System,
14,
17,
22,
94,
108,
118,
145,
179,
194,
195,
203
T
Terms,
24–26,
28,
47,
49,
67,
90,
105,
110–113,
120,
135,
139,
140,
182,
188,
189
Test functions,
18,
23,
25–27,
71,
94,
95,
107,
109,
111,
112,
116,
118,
126,
135–137,
146,
147,
150,
178
Truncation,
15,
21,
23,
25,
27,
28,
72,
106,
107,
111–113,
115–117,
124–126,
146,
185,
186,
188,
189,
209,
217
U
V
Viscous stress tensor,
22,
108
Vitali's convergence theorem,
202,
214
W
Weak solutions,
14,
17,
22,
23,
25,
27,
31,
54,
76,
89–92,
94,
97,
108,
109,
118,
119,
145–147,
169mathematical theory of, ,
101
Y
Young functions,
8–11,
29,
30,
32–34,
36–38,
50,
54–59,
61,
62,
64,
69