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The thin viscous flow equation in higher space dimensions. (English) Zbl 0954.35035
There are proved local integral estimates for nonnegative solutions of the fourth-order degenerate parabolic equation $$u_t+ \text{div}(u^n\nabla\Delta u)= 0$$ in space dimensions two and three. The estimates for solutions of the Cauchy problem and a growth estimate for their support are also proved.

##### MSC:
 35B45 A priori estimates in context of PDEs 35K65 Degenerate parabolic equations 35K55 Nonlinear parabolic equations 35K35 Initial-boundary value problems for higher-order parabolic equations 76D08 Lubrication theory