Some Rigorous Results Concerning Spectral Theory for Ideal Mhd
Some Rigorous Results Concerning Spectral Theory for Ideal Mhd
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It is noteworthy that the boundary condition, B«n =, was not used to establish (118). Thus, from (118) we obtain 2 Re + 2 Re | c' + X, ll(L + XI)ul|2 > IILull^ + Xllul|2 . (124) Moreover, an elementary calculation using the system (77-80) establishes that for X^ sufficiently large there exists d and X so that, if X > Xq llLul|2 + Xllull2 s d{ll-Vp + VxBxB^^||2 + IIV X (vxBq||2 + llV«vl|2 + Xllul|2} (125) We define L_ = L + XI, ^ > ^o X -35- It is clear from the inequality (124) that the norm ...llL_u II is equivalent to the graph norm {IIL_ull^ + llull^}^'^ on D"*" and thus on the closure of X D"*" in this norm. Thus to show that (113) is valid on all of D(L_) we X need merely to show that D"^ is dense in D. For now, assume we have proved this. We are then in a position to conclude the proof that L_ X is a closed operator.
Suppose that (u^, L_Uj^) is a Cauchy sequence in the graph norm.
X Since X is complete, there exist u, V such that u^ ->■ u, Vj^ = L^Uj^ ->• V.
What to read after Some Rigorous Results Concerning Spectral Theory for Ideal Mhd?
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To quickly assess the difficulty of the text, read a short excerpt:
It is noteworthy that the boundary condition, B«n =, was not used to establish (118). Thus, from (118) we obtain 2 Re
Suppose that (u^, L_Uj^) is a Cauchy sequence in the graph norm.
X Since X is complete, there exist u, V such that u^ ->■ u, Vj^ = L^Uj^ ->• V.
What to read after Some Rigorous Results Concerning Spectral Theory for Ideal Mhd?
You can find similar books in the "Read Also" column, or choose other free books by Peter Laurence to read onlineMoreLess
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