Applications to quasilinear evolution equations
Oliver Caps · Teubner-Texte zur Mathematik · 2002
The fifth and last chapter is devoted to applications to quasilinear differential and pseudodifferential evolution equations. In section 5.1 we prove several inequalities that are based on Gagliardo-Moser-Nirenberg estimates, i.e., estimates like $${\left\| {uv} \right\|_{H_q^k}} \leqslant c\left( {{{\left\| u \right\|}_{H_q^k}}{{\left\| v \right\|}_{{L^\infty }\left( {{\mathbb{R}^n}} \right)}} + {{\left\| u \right\|}_{{L^\infty }\left( {{\mathbb{R}^n}} \right)}}{{\left\| v \right\|}_{H_q^k}}} \right).$$