In a previous paper we established a result of high regularity of solutions to a modified p-Stokes problem, p is an element of (1, 2). By this expression we mean a perturbed p-Laplacian system. Here we prove that for a suitable body force there exists at least a solution to a modified p-Navier-Stokes problem, whose regularity is "high". More precisely, without restrictions on the size of the body force, for p close to 2, we prove that there exist second derivatives which are integrable on the whole domain R^3. Of course, the interest of the result is connected to the fact that for the first time a result of high regularity is deduced for solutions to a system of p-Navier-Stokes kind. It is also interesting to point out that the proof, based on the results of the p-Stokes problem, seems to be original and applicable to other nonlinear equations.
A high regularity result of solutions to a modified p-Navier-Stokes system
Crispo, F;Maremonti, P
2016
Abstract
In a previous paper we established a result of high regularity of solutions to a modified p-Stokes problem, p is an element of (1, 2). By this expression we mean a perturbed p-Laplacian system. Here we prove that for a suitable body force there exists at least a solution to a modified p-Navier-Stokes problem, whose regularity is "high". More precisely, without restrictions on the size of the body force, for p close to 2, we prove that there exist second derivatives which are integrable on the whole domain R^3. Of course, the interest of the result is connected to the fact that for the first time a result of high regularity is deduced for solutions to a system of p-Navier-Stokes kind. It is also interesting to point out that the proof, based on the results of the p-Stokes problem, seems to be original and applicable to other nonlinear equations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
