A limit that exists strongly in Sobolev space $H^s$ and weakly in $H^s+1$
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In his paper 'Nonstationary flows of viscous and ideal fluids in $BbbR^3$' Kato mentioned the following: a limit that exists strongly in $H^m-1$ and weakly in $H^m$ what is explicitly the meaning of that convergence? is it simply the following:
$$limlimits_nuto 0|u_nu-u_0|_H^m-1=0~~mboxand ~limlimits_nuto0langle u_nu-u,phirangle_H^m=0,$$
where $phi$ is a test function (well localized and a regular enough function)
Kato, Tosio, Nonstationary flows of viscous and ideal fluids in $R^3$, J. Funct. Anal. 9, 296-305 (1972). ZBL0229.76018.
functional-analysis sobolev-spaces distribution-theory
asked Sep 10 at 17:50
AlphaXY
7232326
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up vote
1
down vote
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In his paper 'Nonstationary flows of viscous and ideal fluids in $BbbR^3$' Kato mentioned the following: a limit that exists strongly in $H^m-1$ and weakly in $H^m$ what is explicitly the meaning of that convergence? is it simply the following:
$$limlimits_nuto 0|u_nu-u_0|_H^m-1=0~~mboxand ~limlimits_nuto0langle u_nu-u,phirangle_H^m=0,$$
where $phi$ is a test function (well localized and a regular enough function)
Kato, Tosio, Nonstationary flows of viscous and ideal fluids in $R^3$, J. Funct. Anal. 9, 296-305 (1972). ZBL0229.76018.
functional-analysis sobolev-spaces distribution-theory
asked Sep 10 at 17:50
AlphaXY
7232326
Yes, it should mean something like that.
– md2perpe
Sep 17 at 19:40
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
In his paper 'Nonstationary flows of viscous and ideal fluids in $BbbR^3$' Kato mentioned the following: a limit that exists strongly in $H^m-1$ and weakly in $H^m$ what is explicitly the meaning of that convergence? is it simply the following:
$$limlimits_nuto 0|u_nu-u_0|_H^m-1=0~~mboxand ~limlimits_nuto0langle u_nu-u,phirangle_H^m=0,$$
where $phi$ is a test function (well localized and a regular enough function)
Kato, Tosio, Nonstationary flows of viscous and ideal fluids in $R^3$, J. Funct. Anal. 9, 296-305 (1972). ZBL0229.76018.
functional-analysis sobolev-spaces distribution-theory
asked Sep 10 at 17:50
AlphaXY
7232326
In his paper 'Nonstationary flows of viscous and ideal fluids in $BbbR^3$' Kato mentioned the following: a limit that exists strongly in $H^m-1$ and weakly in $H^m$ what is explicitly the meaning of that convergence? is it simply the following:
$$limlimits_nuto 0|u_nu-u_0|_H^m-1=0~~mboxand ~limlimits_nuto0langle u_nu-u,phirangle_H^m=0,$$
where $phi$ is a test function (well localized and a regular enough function)
Kato, Tosio, Nonstationary flows of viscous and ideal fluids in $R^3$, J. Funct. Anal. 9, 296-305 (1972). ZBL0229.76018.
functional-analysis sobolev-spaces distribution-theory
functional-analysis sobolev-spaces distribution-theory
asked Sep 10 at 17:50
AlphaXY
7232326
asked Sep 10 at 17:50
AlphaXY
7232326
asked Sep 10 at 17:50
AlphaXY
7232326
asked Sep 10 at 17:50
AlphaXY
7232326
asked Sep 10 at 17:50
AlphaXY
7232326
7232326
Yes, it should mean something like that.
– md2perpe
Sep 17 at 19:40
add a comment |Â
Yes, it should mean something like that.
– md2perpe
Sep 17 at 19:40
Yes, it should mean something like that.
– md2perpe
Sep 17 at 19:40
Yes, it should mean something like that.
– md2perpe
Sep 17 at 19:40
add a comment |Â
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Yes, it should mean something like that.
– md2perpe
Sep 17 at 19:40