$BC1FHJ}Dx<0$G8+$?$h$&$K!"(B $B $B$G$bNc$($P5$BN$NJ}Dx<0$G$O<+A3$J%(%s%H%m%T!<$,B8:_$7!"(B $B$=$l$K$h$C$F40A4$K$O(B Young $BB,EY$r7hDj$G$-$J$$$+$bCN$l$J$$$,(B $B$"$kDxEY$N@-
$BJd40B,EYK!$O6a;w2r$N<}B+$N>ZL@$K;H$o$l$k$,!"(B $B$=$3$G;H$o$l$k6a;w2r$O!"(BGlimm $B$N:9J,6a;w$dGHLLDI@WK!$N$h$&$K(B $B>W7bGH$r6/$/J];}$9$k$h$&$J$b$N$G$O$J$/!"(B $B?M9)G4@-6a;w2r$d(B Lax-Friedrichs $B7?:9J,6a;w2r$N$h$&$K$`$7$m(B $B>W7bGH$r$J$@$i$+$K$9$k$h$&$J$b$N$G$"$k$,!"(B $BNc$($P05=L@-(B Navier-Stokes $BJ}Dx<0$N2r$r05=L@-(B Euler $BJ}Dx<0$KBP$9$k(B $B<+A3G4@-6a;w2r$H$_$F!"(B $B$=$N<}B+@-$rJd40B,EYK!$G>ZL@$G$-$J$$$+$H9M$($F$$$k!#(B
$B$3$N>l9g!"DL>o$NJd40B,EYK!$G$J$/!"(B $B$G$NJd40B,EYK!$NJ}$,(B $B;H$$$d$9$$$@$m$&$H;W$o$l$k$,!"(BEuler $BJ}Dx<0$KBP$9$k(B -$BJd40B,EYK!$G$N(B Tartar $BJ}Dx<0$K4X$9$k8&5f$O8=:_$N$H$3$m$[$H$s$I9T$o$l$F$$$J$$$h$&$G$"$k!#(B
$BNc$($PE57?E*$JHs@~7A?6F0(B
$B$N$h$&$J(B
(
) $B$H$J$k$h$&$JCF@-BN$N(B
$BJ}Dx<0$KBP$7$F$O!"$=$l$,;}$DM-3&@-$O
$B8=:_0lHL$N%P%m%H%m%T%C%/%b%G%k$NJ}Dx<0(B
$B:G6a!"$=$N@)Ls$r$f$k$a$?7k2L$,Aj31,30]) $B$,!"$^$@$+$J$j6/$$>r7o$,$D$$$F$$$k(B $B$h$&$K;W$o$l$k!#(B
$B05NO9`$N7A$r0lHL$K$9$k$H!"%(%s%H%m%T!<$N@-o$O(B Tartar $BJ}Dx<0$r2r$/$?$a$K05NO9`$K$"$kDxEY>r7o$r$D$1(B
$B%(%s%H%m%T!<$,I,MW$J@-/$J$/$9$k!"(B
$B$"$k$$$O6qBNE*$K<0$GI=8=$G$-$k$h$&$J%(%s%H%m%T!<$N$_$G(B
Tartar $BJ}Dx<0$r2r$/!"$H$$$C$?$3$H$O$G$-$J$$$@$m$&$+$H9M$($F$$$k!#(B
DiPerna $B$,;H$C$?%(%s%H%m%T!<$O!"(BDarboux $B$N8x<0$G=q$1$k%(%s%H%m%T!<$G!"(B
Chen, Makino, Lions, Perthame $B$i$b$3$N(B Darboux $B$N8x<0$r85$K$7$F$$$k!#(B
$B$7$+$7!"(B
$B0lJ}$G0lHL$N(B $B$KBP$7$F$bNc$($P(B $B$K4X$7$FB?9`<0$G$"$k(B
$B%(%s%H%m%T!<$O6qBNE*$J<0$GI=8=$9$k$3$H$,$G$-!"(B
$B$3$l$O(B $B$N/$O4K$a$k$3$H$,$G$-$k$N$G$O$J$$$@$m$&$+$H(B
$B9M$($F$$$k!#(B
$B$^$?!"6qBNE*$J(B $B$G$"$C$F$b!"Nc$($P(B Van der Waals $BJ}Dx<0$N(B
$B$h$&$J$b$N$K$D$$$F$O!"0JA0Jd40B,EYK!$K4X$9$k8&5f$b$5$l$?$h$&$@$,(B
(cf. [49])
$B
DiPerna $B$,8e$K;XE&$7$F$$$k$h$&$K(B ([47]) $BI,$:$7$b(B
$B$?$/$5$s$N%(%s%H%m%T!<$OI,MW$G$O$J$/!">/$J$$%(%s%H%m%T!<$G$b$"$kDxEY$N(B
$B7k2L$rF3$/$3$H$,$G$-$k!#(B
$BF1MM$N9M;!$O(B Chen,Lu ([48]) $B$i$K$h$C$F$b;n$_$i$l$F$$$k!#(B
3 $BN$H$_$F(B 1 $B50], Chen,Glimm [51])$B!#(B $B86E@$NFC0[@-$NItJ,$r9MN8$7$??7$?$J6a;w2r(B ($BNc$($P:9J,6a;w2r(B) $B$r9=@.$7$F!"(B $BJd40B,EYK!$rE,MQ$G$-$J$$$+$H9M$($F$$$k!#(B
$B$J$*Jd40B,EYK!$G2r$1$kJ}Dx<0$rA}$d$9!"$H$$$&J}8~$N$[$+$K$b!"(B Tartar $BJ}Dx<0$,2r$+$l$F$$$kJ}Dx<0$KBP$7$F!"(B $B=i4|CM6-3&CMLdBj$d!"30NO9`$dMzNr9`!"JL$JJ}Dx<0$J$I$,DI2C$5$l$?J}Dx<0!"(B $B<~4|2r$NB8:_$J$I$X$NJd40B,EYK!$N1~MQ$J$I$b9T$o$l$F$$$F!"(B $B$=$A$i$NJ}8~$G$N6=L#?<$$OCBj$dL$2r7hLdBj$J$I$b?'!9$"$k!#(B $B$3$l$i$K$D$$$F$O$3$3$G$O>JN,$7!"(B $B$d$d>pJs$,8E$$$,(B [66] $B$r>R2p$9$k$K$H$I$a$k$3$H$H$9$k!#(B