Energy conservation and Onsager's conjecture for a surface growth model
Dynamics of Partial Differential Equations(2023)
Abstract
In this paper, it is shown that the energy equality of weak solution v to a surface growth model is valid if v(x) epsilon L-p(0, T; L-q(T)) with 3/p + 1/q = 1 and 1 <= q <= 4, or v epsilon L-infinity( 0, T; L-infinity( T)), or v(xx) epsilon L-p( 0, T; L-q( T)) with 2/p + 2/5q = 1 and q >= 1, which gives an affirmative answer to a question proposed by Yang in [28, J. Differential Equations 283: 71-84, 2021]. Furthermore, Onsager's conjecture for this model is also considered.
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Key words
Surface growth model,Energy conservation,Onsager's conjecture.
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