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0704.2359.txt |@word masson:1 scm:1 probl:1 interpretation:1 show:3 being:3 indeed:1 results:1 λc:4 proposes:2 spaces:2 relation:3 thanks:7 limites:1 keywords:1 existence:6 satisfies:1 avenue:1 find:2 compact:1 villars:1 now:2 sciences:1 sparrow:1 laminar:2 passage:1 esolution:1 uniqueness:2 verifies:2 transfer:2 easy:1 theorem:8 rham:1 aux:1 ematiques:1 norm:1 bidimensional:1 nonlin:1 above:1 means:3 de:7 appliqu:1 spanned:1 obtain:1 aim:2 liu:1 dx:8 dy:8 integer:1 unique:4 having:1 method:1 erique:1 loss:3 energ:1 ethodes:1 equality:1 hereafter:1 proc:1 arxiv:1 solution:10 ees:1 establishing:1 inequality:1 l2:15 brouwer:2 div:9 fixed:2 streamwise:1 solutions:3 mathematical:1 set:3 λc1:1 opposed:1 formulate:1 ed:1 uses:1 product:1 operator:1 see:7 num:1 pour:1 w1:1 quelques:1 etique:1 extract:1 es:1 techniques:1 bilinear:1 provided:1 hilbert:1 satisfying:3 developed:1 umr:1 establish:2 section:1 since:3 area:1 calcul:1 finally:1 λn:1 deduces:3 vector:2 decomposition:1 closed:1 pn:3 formula:2 boundary:2 three:1 conditions:2 checks:3 math:3 shows:1 coefficient:1 galerkin:1 theory:1 initially:3 equivalent:2 each:1 pp:2 here:1 pressure:5 les:2 eaires:1 wi:3 wm:1 additive:3 estimate:3 equations:6 universit:2 takes:3 stokes:10 remark:2 r2:1 geometry:1 study:2 vectors:1 introduces:1 pe1:2 raviart:1 thermique:1 place:2 navier:6 connected:2 consequently:2 tome:1 separable:1 ch:1 point:1 apr:1 pays:1 h1:5 λe1:1 except:1 dimensional:2 references:1 coercive:1 moreover:6 arbitrary:1 u2:8 open:2 considers:2 methods:1 given:3 checked:2 exists:7 basis:1 introduction:1 e1:1 there:9 u1:5 approximate:2 least:1 france:1 belongs:1 lions:2 therefore:1 series:1 gim:2 gauthier:1 sections:1 pm:4 function:1 north:1 duality:1 form:1 incompressible:2 subspace:1 modelling:1 heat:2 weakly:1 external:1 particular:2 known:1 imbedding:1 present:1 springer:1 holland:1 recall:1 inside:2 des:2 variations:1 up:1 us:8 will:2 temam:1 subsequence:1 praha:1 limit:1 compactness:1 represents:1 following:1 problem:17 enables:1 amsterdam:1 constructs:1 proof:2 constant:4 lax:1 figure:2 give:1 defined:1 h00:3 abstract:1 sectional:1 thus:5 vm:5 according:2 ii:3 ap:1 assumptions:1 sense:1 follows:1 inf:2 emes:1 defines:2 again:1 pau:2 journal:1 girault:2 cross:1 poincar:1 note:4 application:1 periodic:5 arguments:1 green:2 finite:1 channel:4 uν:2 cnrs:1 continuous:2 normal:1 laboratoire:2 what:1 fluid:2 v1:13 plane:1 bounded:1 but:2 ducts:1 hilbertian:1 analyse:1 data:1 jean:1 shown:1 ematique:1 um:11 short:1 fully:1 considered:1 makes:1 clear:2 space:4 flow:3 dσ:6 analysis:1 element:1 bracket:1 so:3 easily:2 milgram:1 model:1 resolution:1 dimension:2 |
0704.2360.txt |@word scm:1 concept:1 sci:1 consider:3 eaires:1 results:1 scalar:1 proposition:2 limites:2 rot:2 reasoning:1 compact:3 dunod:2 paris:2 aum:21 uniqueness:2 present:1 under:1 aux:3 norm:1 orthogonal:1 fac:1 voir:1 condition:4 tokyo:1 wm0:1 solution:20 t0:26 science:1 small:4 div:17 magenes:2 des:5 estimates:10 zero:2 nonhomogeneous:2 quelques:1 nonlinear:2 temam:3 giving:1 sum:3 overload:1 establishes:1 sup:4 new:1 increasing:1 method:1 seeks:2 satisfy:4 processing:1 deduces:7 respectively:3 here:1 arch:1 strong:5 equations:11 change:1 contraction:1 obtained:1 remark:4 generalizing:1 glm:1 study:1 allows:1 contradiction:1 periodic:1 products:1 projection:1 classification:1 apr:1 unif:1 hardy:1 vols:1 establish:3 use:1 takes:3 esolution:1 recalling:1 positive:1 finally:2 ψt:1 hilbert:1 therefore:3 etude:1 more:1 knows:3 becomes:3 berlin:1 particular:1 iii:2 springer:3 integrating:1 h10:5 recall:4 work:1 hopf:1 unknowns:1 following:9 example:1 proof:9 νt:3 neglected:1 assumptions:3 numbers:1 νc:3 respective:1 holds:2 navierstokes:2 max:1 fluid:2 france:1 data:2 element:1 hypotheses:5 so:6 sect:1 order:1 fε:3 over:3 paper:1 existence:8 satisfies:5 avenue:1 takeshita:2 li:1 choose:1 pays:2 main:1 non:2 appliqu:1 introduce:2 now:8 above:2 2t:2 term:1 ethodes:1 verifying:1 sufficiently:3 l4:17 inequality:6 l2:63 breach:1 l1:1 universit:4 2i:1 homogeneous:1 domain:3 differential:1 ed:1 combining:1 es:2 out:1 integrates:1 since:3 math:4 shows:2 theory:3 applications:1 estimate:3 definition:1 r2:1 r3:1 linearized:1 place:2 gordon:1 navier:8 consequence:2 first:4 initial:2 approximate:2 multiplying:1 another:1 precisely:1 open:3 given:5 their:1 introduction:2 unknown:1 system:6 indicate:1 calculations:1 incompressible:3 mech:1 norms:1 holland:1 showed:1 second:1 raviart:2 subsequence:1 supposed:1 naturally:1 result:3 rat:1 manner:1 need:1 north:1 emes:2 gagliardo:2 facult:1 depending:2 lim:1 able:2 note:5 sciences:1 forces:2 begin:2 towards:1 object:1 thermique:1 multiply:5 class:1 clear:3 flow:1 exp:3 its:1 probl:2 show:1 notations:2 spaces:4 relation:1 solutions:7 enes:1 cnrs:1 state:1 aubin:1 lemma:27 only:1 integrate:1 announce:1 ematiques:1 nonlin:1 ladyzhenskaya:2 notation:2 get:1 dependent:1 de:11 uε0:15 etrique:1 words:1 dt:22 ds:12 qt:28 approach:1 arxiv:1 remove:1 fixed:3 set:1 exists:12 see:4 num:1 w2:4 w1:3 w0:4 subject:1 satisfying:7 eigenfunctions:1 tend:1 enough:1 smallest:1 boundary:8 conditions:4 hence:1 galerkin:1 ends:2 terms:1 wm:2 wj:5 reproduces:1 hypothesis:1 key:1 amer:1 last:1 repeating:1 σm:2 taking:1 according:6 embedding:1 σt:25 ch:1 point:2 dimensional:1 moreover:5 considers:1 considering:1 pp:3 belongs:1 ph:1 define:1 corresponding:1 external:2 c3:5 c2:3 c1:11 c6:8 c5:6 c4:2 case:1 value:1 will:2 suppose:7 compactness:1 au:31 property:4 vol:3 vi:1 thus:8 ii:4 im:1 ia:1 technology:1 pau:3 make:1 girault:2 35k:1 same:6 verifies:1 finite:1 independent:2 used:1 laboratoire:2 numerical:1 hand:2 v0:13 interested:1 weakly:5 older:1 analysis:3 solve:1 jean:1 dimension:1 being:6 obtain:1 thanks:5 λj:1 setting:2 theorem:12 doctorat:1 erique:1 depends:1 using:2 unique:10 energ:1 necessary:1 follows:6 unnecessary:1 ees:1 gjm:5 yields:2 recalls:1 mathematical:3 right:1 methods:2 sequence:5 gε:82 respect:1 etique:1 provided:1 dense:1 dimensions:2 umr:1 univ:1 avoid:1 does:1 equibounded:4 proc:1 semigroups:1 bm:3 each:1 pressure:2 step:3 br:3 properties:2 cε:5 stokes:10 extension:1 o:2 side:1 remains:2 consequently:3 other:1 soc:1 h2:27 h3:20 h1:41 functional:1 en:1 references:1 operator:3 amsterdam:1 next:2 u0m:6 nirenberg:2 topologies:1 support:1 there:12 u0:11 lions:7 way:4 series:2 solonnikov:2 gim:4 viscous:1 dx:4 m0:2 function:10 gronwall:2 hr:5 hs:2 but:6 construction:1 true:1 etrie:1 made:1 reproductive:10 smooth:3 up:2 us:18 um:67 limit:1 problem:10 strongly:1 associated:1 defined:1 abstract:1 transl:1 ap:1 single:1 exist:1 az:10 defines:2 again:1 functions:2 ematique:1 when:2 application:1 valid:2 mathematics:1 galdi:2 bounded:2 variable:1 implies:1 homog:1 assume:1 eom:1 time:2 |
0704.2361.txt |@word scm:1 probl:13 sci:1 enes:3 ede:3 puis:2 results:1 appliquons:1 comme:2 emonstration:2 paper:1 erifie:2 solutions:2 limites:5 banach:1 afin:1 existence:2 obtenir:1 faible:5 avenue:1 c1:1 compact:1 dunod:2 egulier:1 le:18 mais:1 la:13 series:1 voir:1 passage:1 corollaire:1 source:1 chaque:1 lemme:5 lp:10 notons:1 aux:6 suit:1 ematiques:1 ailleurs:2 adapt:1 nouveau:2 non:2 nonlin:1 ladyzhenskaya:1 navierstokes:1 syst:3 montrer:2 de:57 injection:3 appliqu:1 esultat:3 ϕm:2 ethodes:1 sont:1 peut:3 dx:1 lui:1 ensuite:1 fac:1 devient:1 du:5 ethode:1 ds:3 eme:17 energ:1 finite:1 qu:2 qt:5 erature:3 proc:1 arxiv:1 solution:10 vitesse:1 ecrit:2 viscous:1 approch:1 continue:1 l2:50 breach:1 l1:1 2l:1 references:1 universit:2 magenes:1 mathematical:1 emes:2 en:12 tel:3 methods:1 assur:1 ed:1 energy:1 some:1 espaces:1 existe:5 born:10 second:1 b0:5 ees:1 nonhomogeneous:1 λj:8 etique:1 es:6 ouvert:2 efinie:1 passons:1 ici:2 est:10 utilise:1 umr:1 esulte:1 sorte:3 takeshita:1 equent:2 efinit:2 αc:2 gjm:4 µi:1 sur:29 energie:3 µj:5 si:3 chaleur:2 boundary:1 fluide:3 conditions:4 cela:1 math:2 galerkin:1 esultats:1 compacte:3 theory:2 convergences:1 pose:1 tels:1 erifiant:2 base:4 que:23 etudier:1 qui:1 equations:7 div:2 stong:1 stokes:6 unique:7 enoncer:1 esolution:2 utilisant:2 applications:1 esoudre:1 o:9 espace:2 limite:3 paris:2 les:3 plus:1 une:12 δij:1 navier:6 estimation:3 quelques:1 adjoint:1 σt:2 vitesses:1 ψm:2 simplifier:2 ch:1 admet:3 cl:1 apr:2 pays:1 variables:1 vient:1 mech:1 ce:2 dimensional:1 outre:1 cons:2 champ:1 pp:2 lieu:2 amsterdam:1 u2:2 univ:1 donn:4 passer:1 poss:3 hk:6 propose:1 ψk:2 introduction:1 avec:8 esente:1 u1:2 emontrer:1 france:1 ψj:19 ee:7 ψi:3 lions:3 reproductive:2 ecriture:1 posant:2 suivantes:1 δjk:3 propres:1 θk:11 telle:4 gronwall:1 th:3 form:1 θm:64 forc:1 incompressible:2 trois:1 eduit:4 erateur:2 compacit:1 finalement:3 h2:4 suite:3 convergence:1 θs:15 θp:4 lorsque:3 iii:1 northholland:1 fort:1 springer:1 pi:1 choix:1 temp:3 soit:5 fortes:1 equation:5 des:4 dans:31 pour:14 raviart:1 temam:2 sous:1 un:2 suppose:4 dv:1 property:2 encore:1 b1:4 remarque:3 f1:2 f2:2 sp:1 associated:1 give:1 int:4 flow:1 abstract:1 ram:2 vers:1 lin:1 ii:1 ap:1 rat:1 mots:1 au:3 il:11 dθ:1 ia:1 analysis:2 convection:2 suivant:4 clair:2 particulier:3 eels:2 par:10 pas:1 pau:2 lim:1 alors:8 girault:1 vecteurs:1 lp1:1 lp0:2 note:1 dt:10 fonction:1 auto:1 tout:7 er:1 mˆeme:1 gordon:1 cnrs:1 allons:1 orthogonale:1 laboratoire:2 etant:3 grˆace:2 repr:1 eaire:1 membre:1 thermique:2 maintenant:2 consid:2 utiliser:1 eciale:1 arch:1 eaires:1 ene:2 satisfait:1 tokyo:1 permet:1 erons:1 entre:3 obtient:3 homog:3 classe:1 erieure:1 egration:1 lequel:1 element:1 iv:1 eor:3 ext:1 sect:1 donc:5 nous:2 jean:1 op:2 dimension:1 se:3 vol:1 |
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