That's a very good question - and as all good questions it's difficult to answer: it depends. :)
There was recently a case where Håkan Lans argued he should not have to pay Acer after having lost a patent suit in Washington, because he is a Swedish citizen and the american verdict was according to him unjust. He first lost, but appealed and won in the appellate court (Hovrätten) [1]. The court argued that since there was no contract between the parties governing jurisdiction the foreign court decision could not be used in a Swedish court as proof of debt. Therefore Acer would have to sue Håkan Lans in Sweden, and have a Swedish court rule on the merits of the case, if they wanted the aid of Swedish authorities in collecting damages.
There was recently a case where Håkan Lans argued he should not have to pay Acer after having lost a patent suit in Washington, because he is a Swedish citizen and the american verdict was according to him unjust. He first lost, but appealed and won in the appellate court (Hovrätten) [1]. The court argued that since there was no contract between the parties governing jurisdiction the foreign court decision could not be used in a Swedish court as proof of debt. Therefore Acer would have to sue Håkan Lans in Sweden, and have a Swedish court rule on the merits of the case, if they wanted the aid of Swedish authorities in collecting damages.
[1] http://www.nyteknik.se/nyheter/it_telekom/datorer/article250...