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EnglishThe authors consider weak solutions u = (u1, u2, · · · , un) 2 H1( !Rn) of nonlinear equations in the following form: DA i (x, u,ru)+Bi(x, u,ru) = −(rp)i (i = 1, · · · , n) and r · u = g, where g is suitably smooth and p 2 L2( ! R). The matrix A i satisfies an ellipticity condition, and growth conditions for A i and Bi with respect to u and |ru| are given. Regularity is considered for the linear, semilinear, quasilinear, and nonlinear cases with decreasing results as the equation becomes more difficult. The known results for the Navier-Stokes equations when n >=4 are derived in a new fashion.
http://hdl.handle.net/11384/5983| Titolo: | Nonlinear systems of the type of the stationary Navier- Stokes system |
| Autori interni: | GIAQUINTA, Mariano |
| Data di pubblicazione: | 1982 |
| Rivista: | JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK |
| Abstract: | The authors consider weak solutions u = (u1, u2, · · · , un) 2 H1( !Rn) of nonlinear equations in the following form: DA i (x, u,ru)+Bi(x, u,ru) = −(rp)i (i = 1, · · · , n) and r · u = g, where g is suitably smooth and p 2 L2( ! R). The matrix A i satisfies an ellipticity condition, and growth conditions for A i and Bi with respect to u and |ru| are given. Regularity is considered for the linear, semilinear, quasilinear, and nonlinear cases with decreasing results as the equation becomes more difficult. The known results for the Navier-Stokes equations when n >=4 are derived in a new fashion. |
| Handle: | http://hdl.handle.net/11384/5983 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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